  Vector $SO(3)$ gauged $O(4)$ sigma models on $\R_3$ are presented. The
topological charge supplying the lower bound on the energy and rendering the
soliton stable coincides with the Baryon number of the Skyrmion. These solitons
have vanishing magnetic monopole flux. To exhibit the existence of such
solitons, the equations of motion of one of these models is integrated
numerically. The structure of the conserved Baryon current is briefly
discussed.
