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"

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.