We compute the current as a function of voltage for resonant tunneling through an Anderson impurity in the low-temperature, Kondo, regime. The differential conductance curve has the same structure as the zero-bias spectral function, but is sharper because a finite voltage tends to destroy the Kondo resonance. This destruction of the Kondo resonance cannot be mapped onto an increase in the effective temperature at the impurity site. The calculation is performed in the symmetric Anderson model using perturbation theory in the Hubbard U repulsion.