The Collaborative International Dictionary of English v.0.48:

Delicacy \Del"i*ca*cy\, n.; pl. Delicacies. [From Delicate,
   a.]
   1. The state or condition of being delicate; agreeableness to
      the senses; delightfulness; as, delicacy of flavor, of
      odor, and the like.
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            What choice to choose for delicacy best. --Milton.
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   2. Nicety or fineness of form, texture, or constitution;
      softness; elegance; smoothness; tenderness; and hence,
      frailty or weakness; as, the delicacy of a fiber or a
      thread; delicacy of a hand or of the human form; delicacy
      of the skin; delicacy of frame.
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   3. Nice propriety of manners or conduct; susceptibility or
      tenderness of feeling; refinement; fastidiousness; and
      hence, in an exaggerated sense, effeminacy; as, great
      delicacy of behavior; delicacy in doing a kindness;
      delicacy of character that unfits for earnest action.
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            You know your mother's delicacy in this point.
                                                  --Cowper.
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   4. Addiction to pleasure; luxury; daintiness; indulgence;
      luxurious or voluptuous treatment.
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            And to those dainty limbs which Nature lent
            For gentle usage and soft delicacy?   --Milton.
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   5. Nice and refined perception and discrimination; critical
      niceness; fastidious accuracy.
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            That Augustan delicacy of taste which is the boast
            of the great public schools of England. --Macaulay.
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   6. The state of being affected by slight causes;
      sensitiveness; as, the delicacy of a chemist's balance.
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   7. That which is alluring, delicate, or refined; a luxury or
      pleasure; something pleasant to the senses, especially to
      the sense of taste; a dainty; as, delicacies of the table.
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            The merchants of the earth are waxed rich through
            the abundance of her delicacies.      --Rev. xviii.
                                                  3.
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   8. Pleasure; gratification; delight. [Obs.]
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            He Rome brent for his delicacie.      --Chaucer.

   Syn: See Dainty.
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WordNet (r) 3.0 (2006):

delicacy
    n 1: the quality of being beautiful and delicate in appearance;
         "the daintiness of her touch"; "the fineness of her
         features" [syn: daintiness, delicacy, fineness]
    2: something considered choice to eat [syn: dainty,
       delicacy, goody, kickshaw, treat]
    3: refined taste; tact [syn: delicacy, discretion]
    4: smallness of stature [syn: delicacy, slightness]
    5: lack of physical strength [syn: fragility, delicacy]
    6: subtly skillful handling of a situation [syn: delicacy,
       diplomacy, discreetness, finesse]
    7: lightness in movement or manner [syn: airiness, delicacy]

Moby Thesaurus II by Grady Ward, 1.0:

385 Moby Thesaurus words for "delicacy":
   absoluteness, accommodatingness, accuracy, acquired taste,
   affectivity, agreeableness, airiness, airy texture, allergy,
   ambrosia, amiable weakness, anaphylaxis, appreciation,
   appreciation of differences, appreciation of excellence,
   appreciativeness, artistic judgment, ascent, attention to detail,
   attention to fact, attentiveness, attenuation, banquet, beauty,
   bonne bouche, breakability, breakableness, brittleness, bubbliness,
   buoyancy, cachexia, cachexy, care for truth, cate, chanciness,
   changeableness, choice morsel, choiceness, chronic ill health,
   circumstantiality, civilized taste, civilizedness, collapse,
   complaisance, concern, connoisseurship, conscientiousness,
   considerateness, consideration, correctness, cosseting,
   crackability, crackableness, crispness, critical niceness,
   criticality, criticalness, crumbliness, crushability,
   crushableness, cultivated taste, cultivation, culture, cunningness,
   cuteness, daintiness, dainty, debilitation, debility, decency,
   decorousness, decorum, decrepitude, delicate distinction,
   delicate health, delicateness, dessert, destructibility, detail,
   diaphanousness, differentia, differential, difficulty, dilutedness,
   dilution, diminutiveness, discriminating taste, discriminatingness,
   discrimination, discriminativeness, disintegration, distinction,
   doubtfulness, down, downiness, dubiousness, easiness, effeminacy,
   elegance, empathy, enervation, ethereality, exactingness,
   exactitude, exactness, excellence, exhaustion, exiguity,
   exiguousness, exility, exquisiteness, faithfulness, fastidiousness,
   faultlessness, feast, featheriness, feebleness, feel, feeling,
   fewness, fidelity, filminess, fine palate, fine point,
   fine-grainedness, fineness, finesse, finicality, finicalness,
   finickiness, finickingness, fissility, flawlessness, flimsiness,
   floatability, flossiness, fluff, fluffiness, foaminess, fondness,
   fracturableness, fragility, frailness, frailty, frangibility,
   friability, frothiness, fussiness, fuzz, fuzziness, gauziness,
   gentleness, good taste, goody, gossameriness, grace, gracefulness,
   gracility, graciosity, graciousness, hairline, hazardousness,
   healthlessness, heedfulness, helpfulness, human frailty,
   hyperesthesia, hyperpathia, hypersensitivity, hypochondria,
   hypochondriasis, identification, ill health, impressionability,
   inconsequentiality, inconsiderableness, indecisiveness, indulgence,
   infirmity, infirmity of will, inherent vice, insecurity,
   insignificance, insolidity, instability, insubstantiality,
   insufficiency, invalidism, invalidity, irresolution, irritability,
   judiciousness, laciness, lack of weight, languishing, languishment,
   leniency, levitation, levity, lightness, literalism, literality,
   literalness, littleness, luxury, making distinctions, manna,
   margin, mathematical precision, meagerness, meanness, mellowness,
   meticulousness, mindfulness, minuteness, mistiness, moderateness,
   modesty, moral weakness, morbidezza, morbidity, morbidness, morsel,
   narrow margin, nectar, nervousness, nice distinction, niceness,
   niceness of distinction, nicety, nonresistiveness, nonrigidity,
   nuance, obligingness, oversensibility, oversensitiveness,
   overtenderness, palate, paperiness, particle of difference,
   particularity, particularness, passibility, peach fuzz, peakedness,
   perceptiveness, perceptivity, perfection, perilousness, pettiness,
   photophobia, picayunishness, plushiness, point of difference,
   polish, poor health, precariousness, preciseness, precisianism,
   precision, prickliness, propriety, pubescence, pudency, pudicity,
   pulpiness, punctiliousness, punctuality, puniness, quality, rarity,
   refined discrimination, refined palate, refinement, regale, regard,
   regardfulness, responsiveness, right, rightness, rigidity,
   rigidness, rigor, rigorousness, riskiness, satin, satininess,
   savory, scantiness, scrupulosity, scrupulousness, seemliness,
   selectiveness, sense, sensibility, sensitiveness, sensitivity,
   sensitization, severity, shade of difference, shakiness, shame,
   sickliness, silk, silkiness, sleaziness, slenderness, slightness,
   slimness, slipperiness, smallness, smoothness, softheartedness,
   softness, solicitousness, solicitude, sophistication, soreness,
   sponginess, strictness, subtility, subtle distinction, subtlety,
   supersensitivity, susceptibility, sweetmeat, sword of Damocles,
   tact, tactfulness, taste, tastefulness, tender feeling,
   tenderheartedness, tenderness, tenuity, tetchiness, textualism,
   the letter, thin skin, thinness, thought, thoughtfulness,
   ticklish business, ticklishness, tidbit, tininess, titbit,
   toleration, totteriness, touchiness, treat, triviality,
   uncertainty, undependability, unhealthiness, unheaviness,
   unimportance, unpredictability, unreliability, unsafeness,
   unsolidity, unsoundness, unsteadiness, unsubstantiality,
   unsureness, untrustworthiness, unwholesomeness, vagueness,
   valetudinarianism, velleity, velvet, velvetiness, volatility,
   vulnerability, warm heart, warmheartedness, wasting, wateriness,
   weakliness, weakness, weightlessness, wide margin, wispiness,
   womanishness, yeastiness