  We study the quadrupole oscillation of a Bose-Einstein condensate of
$^{87}$Rb atoms confined in an axisymmetric magnetic trap, after it has been
stirred by an auxiliary laser beam. The stirring may lead to the nucleation of
one or more vortices, whose presence is revealed unambiguously by the
precession of the axes of the quadrupolar mode. For a stirring frequency
$\Omega$ below the single vortex nucleation threshold $\Omega_c$, no measurable
precession occurs. Just above $\Omega_c$, the angular momentum deduced from the
precession is $\sim \hbar$. For stirring frequencies above $\Omega_c$ the
angular momentum is a smooth and increasing function of $\Omega$, until an
angular frequency $\Omega_c'$ is reached at which the vortex lattice disappears
and the precession stops.
