  The Casimir force between parallel lines in a theory describing condensed
vortices in a plane is determined. We make use of the relation between a
Chern-Simons-Higgs model and its dualized version, which is expressed in terms
of a dual gauge field and a vortex field. The dual model can have a phase of
condensed vortices and, in this phase, there is a mapping to a model of two
non-interacting massive scalar fields from which the Casimir force can readily
be obtained. The choice of boundary conditions required for the mapped scalar
fields and their association with those for the vectorial field and the issues
involved are discussed. We also briefly discuss the implications of our results
for experiments related to the Casimir effect when vortices can be present.
