Using a focused laser beam we stir a Bose-Einstein condensate of Rb-87 conf
ined in a magnetic trap and observe the formation of a vortex for a stirrin
g frequency exceeding a critical value. At larger rotation frequencies we p
roduce states of the condensate for which up to four vortices are simultane
ously present. We have also measured the lifetime of the single vortex stat
e after turning off the stirring laser beam.