  We examine the effects of the CuO chains on the density of states in the
vortex phase in YBa_2Cu_3O_7, via a calculation based on the tight-binding
proximity model. In this model, chain superconductivity results from
single-electron hopping between the intrinsically-normal chains and
intrinsically-superconducting CuO_2 planes. The calculations are based on
self-consistent solutions of the Bogolyubov-de Gennes equations for a bilayer
consisting of a single CuO_2 layer and a single CuO chain layer. We find that,
in addition to the dispersing resonances found in single-layer models, the
chains introduce a second set of dispersing resonances associated with the
induced gap in the chain layer. These new resonances are highly anisotropic and
distort the vortex core shape.
