We study the locality properties of the vortex operators in compact U(1) Maxwell-Chern-Simons and SU(N) Yang-Mills-Chem-Simons theories in 2+1 dimensions. We find that these theories do admit local vortex operators and thus in the UV regularized versions should contain stable magnetic vortices. In the continuum limit however the energy of these vortex excitations generically is logarithmically UV divergent. Nevertheless the classical analysis shows that at small values of the CS coefficient kappa the vortices become light. It is conceivable that they in fact become massless and condense due to quantum effects below some small kappa. If this happens the magnetic symmetry breaks spontaneously and the theory is confining.