Vector SO(3) gauged O(4) sigma models on R(3) are presented. The topol
ogical charge supplying the lower bound on the energy and rendering th
e soliton stable coincides with the baryon number of the Skyrmion. The
se solitons have vanishing magnetic monopole flux. To exhibit the exis
tence of such solitons, the equations of motion of one of these models
are integrated numerically. The structure of the conserved baryon cur
rent is briefly discussed.