We have developed an evaporative cooling technique that accelerates the rot
ation of an ultracold Rb-87 gas, confined in a static harmonic potential. A
s a normal gas is evaporatively spun up and cooled below quantum degeneracy
, it is found to nucleate vorticity in a Bose-Einstein condensate. Measurem
ents of the condensate's aspect ratio and surface-wave excitations are cons
istent with effective rigid-body rotation. Rotation rates of up to 94% of t
he centrifugal limit are inferred. A threshold in the normal cloud's rotati
on is observed for the intrinsic nucleation of the first vortex. The thresh
old value lies below the prediction for a nucleation mechanism involving th
e excitation of surface waves of the condensate.