The Collaborative International Dictionary of English v.0.48:

Highly \High"ly\, adv.
   In a high manner, or to a high degree; very much; as, highly
   esteemed.
   [1913 Webster]

WordNet (r) 3.0 (2006):

highly
    adv 1: to a high degree or extent; favorably or with much
           respect; "highly successful"; "He spoke highly of her";
           "does not think highly of his writing"; "extremely
           interesting" [syn: highly, extremely]
    2: at a high rate or wage; "highly paid workers"
    3: in a high position or level or rank; "details known by only a
       few highly placed persons"

Moby Thesaurus II by Grady Ward, 1.0:

54 Moby Thesaurus words for "highly":
   a deal, a great deal, a lot, abundantly, approvingly,
   as all creation, as all get-out, authoritatively, beaucoup,
   considerable, considerably, decidedly, effectively,
   enthusiastically, ever so, ever so much, exceedingly,
   exceptionally, extraordinarily, extremely, favorably, galore,
   greatly, hugely, immensely, importantly, in great measure,
   incomparably, influentially, largely, much, muchly, never so,
   no end, no end of, not a little, notably, parlous, plenty,
   powerfully, pretty much, quite, remarkably, so, so very much,
   strikingly, strongly, surpassingly, to the skies, tremendously,
   very, very much, warmly, well



The Jargon File (version 4.4.7, 29 Dec 2003):

highly
 adv.

    [scientific computation] The preferred modifier for overstating an
    understatement. As in: highly nonoptimal, the worst possible way to do
    something; highly nontrivial, either impossible or requiring a major
    research project; highly nonlinear, completely erratic and unpredictable;
    highly nontechnical, drivel written for lusers, oversimplified to the
    point of being misleading or incorrect (compare drool-proof paper). In
    other computing cultures, postfixing of in the extreme might be
    preferred.