  We study a spontaneously broken SU(2) Chern-Simons-Higgs model coupled though
a Higgs portal to an uncharged triplet scalar with a vacuum state competing
with the Higgs one. We find vortex-like solutions to the field equations in
different parameter space regions. Depending on the scalar coupling constants
we find a parameter region in which the competing order creates a halo about
the Chern-Simons-Higgs vortex core, together with two other regions, one where
no vortex solutions exist, the other where ordinary Chern-Simons-Higgs vortices
can be found. We derive the low-energy theory for the moduli fields on the
vortex world sheet and also discuss the connection of our results with those
found in studies of competing orders in high temperature superconductors.
