The Collaborative International Dictionary of English v.0.48:

Apace \A*pace"\, adv. [Pref. a- + pace. OE. a pas at a walk, in
   which a is the article. See Pace.]
   With a quick pace; quick; fast; speedily.
   [1913 Webster]

         His dewy locks did drop with brine apace. --Spenser.
   [1913 Webster]

         A visible triumph of the gospel draw? on apace. --I.
   Taylor.
   [1913 Webster]

WordNet (r) 3.0 (2006):

apace
    adv 1: with rapid movements; "he works quickly" [syn: quickly,
           rapidly, speedily, chop-chop, apace] [ant:
           easy, slow, slowly, tardily]

Moby Thesaurus II by Grady Ward, 1.0:

75 Moby Thesaurus words for "apace":
   PDQ, amain, at flank speed, at once, by forced marches, cursorily,
   decisively, directly, double-quick, expeditiously, fast,
   feverishly, flat-out, forthwith, furiously, hand over fist,
   hand over hand, hastily, hell for leather, hell-bent,
   hell-bent for election, helter-skelter, hotfoot, hurriedly,
   hurry-scurry, immediately, in double time, in double-quick time,
   in high, in high gear, in no time, in passing,
   in seven-league boots, instanter, instantly, lickety-cut,
   lickety-split, on the double, on the instant, on the run,
   on the spot, pell-mell, post, posthaste, pretty damned quick,
   promptly, pronto, quick, quickly, rapidly, right away, right off,
   slapdash, smartly, snappily, speedily, straightaway, straightway,
   subito, summarily, superficially, swiftly, trippingly,
   under forced draft, whip and spur, with a rush, with all haste,
   with all speed, with dispatch, with giant strides, with haste,
   with rapid strides, with speed, without delay,
   without further delay