The Collaborative International Dictionary of English v.0.48:

Raceme \Ra*ceme"\ (r[.a]*s[=e]m"; 277), n. [L. racemus a bunch
   of berries, a cluster of grapes. See Raisin.] (Bot.)
   A flower cluster with an elongated axis and many one-flowered
   lateral pedicels, as in the currant and chokecherry.
   [1913 Webster]

   Compound raceme, one having the lower pedicels developed
      into secondary racemes.
      [1913 Webster]

WordNet (r) 3.0 (2006):

raceme
    n 1: usually elongate cluster of flowers along the main stem in
         which the flowers at the base open first