We find that Kondo resonant conductance can occur in a quantum dot in the C
oulomb blockade regime with an even number of electrons N. The contacts are
attached to the dot in a pillar configuration, and a magnetic field B-perp
endicular to along the axis is applied. B-perpendicular to lifts the spin d
egeneracy of the dot energies. Usually, this prevents the system from devel
oping the Kondo effect. Tuning B-perpendicular to to the value B* where lev
els with different total spin cross restores both the degeneracy and the Ko
ndo effect. We analyze a dot charged with N = 2 electrons. Coupling to the
contacts is antiferromagnetic due to a spin selection rule and, in the Kond
o state, the charge is unchanged while the total spin on the dot is S = 1/2
.