The Collaborative International Dictionary of English v.0.48:

Openly \O"pen*ly\, adv. [AS. openlice.]
   1. In an open manner; publicly; not in private; without
      secrecy.
      [1913 Webster]

            How grossly and openly do many of us contradict the
            precepts of the gospel by our ungodliness!
                                                  --Tillotson.
      [1913 Webster]

   2. Without reserve or disguise; plainly; evidently.
      [1913 Webster]

            My love . . . shall show itself more openly. --Shak.
      [1913 Webster]

WordNet (r) 3.0 (2006):

openly
    adv 1: in an open way; "he openly flaunted his affection for his
           sister"

Moby Thesaurus II by Grady Ward, 1.0:

115 Moby Thesaurus words for "openly":
   abominably, aboveboard, agonizingly, all joking aside, apparently,
   artlessly, audaciously, awfully, baldly, balefully, before one,
   bitterly, blatantly, bluffly, bluntly, boldly, brashly, brazenly,
   broadly, brusquely, candidly, confoundedly, cruelly, damnably,
   deadly, deathly, deucedly, directly, distressingly, dolorously,
   dreadfully, egregiously, excessively, excruciatingly, exorbitantly,
   exteriorly, externally, extravagantly, face to face, flagrantly,
   flauntingly, frankly, freely, frightfully, genuinely, grievously,
   guilelessly, hellishly, horribly, improperly, in all conscience,
   in all seriousness, in broad daylight, in open court,
   in plain English, in plain sight, in plain view, in plain words,
   in public, in public view, in the limelight, in the marketplace,
   in the open, inexcusably, infernally, ingenuously, inordinately,
   intolerably, lamentably, miserably, nakedly, naturally,
   on the outside, on the surface, on the table, openheartedly, out,
   outright, outside, outspokenly, outwardly, outwards, overtly,
   painfully, piteously, plain-spokenly, plainly, publically,
   publicly, roundly, sadly, shatteringly, shockingly, simply,
   sincerely, something awful, something fierce, sorely, staggeringly,
   straightforwardly, superficially, terribly, to all appearances,
   torturously, unashamedly, unbearably, unconscionably,
   unconstrainedly, unduly, unpardonably, unreservedly,
   unrestrainedly, with no nonsense, without, woefully