  We have observed the persistent flow of Bose-condensed atoms in a toroidal
trap. The flow persists without decay for up to 10 s, limited only by
experimental factors such as drift and trap lifetime. The quantized rotation
was initiated by transferring one unit, $\hbar$, of the orbital angular
momentum from Laguerre-Gaussian photons to each atom. Stable flow was only
possible when the trap was multiply-connected, and was observed with a BEC
fraction as small as 15%. We also created flow with two units of angular
momentum, and observed its splitting into two singly-charged vortices when the
trap geometry was changed from multiply- to simply-connected.
