  Using a semi-analytic model based on the Thomas-Fermi approximation, we
investigate the relevance of the quadrupole deformation of a trapped
Bose-Einstein condensate for the nucleation of quantized vortices. For
sufficiently high angular velocities $\Omega$ of the trap, the tendency of the
system to exhibit spontaneous deformation is shown to lower the barrier which
inhibits the nucleation of vortices at smaller $\Omega$. The corresponding
value of the critical angular velocity $\Omega_c$ is calculated as a function
of the deformation of the trap and of the chemical potential. The theoretical
predictions for $\Omega_c$ refer to the case of a sudden switch-on of the
deformed rotating trap and they are compared with recent experimental data.
