  We couple in superspace a `dual' vector multiplet (C_{m_1... m_7}, \l^\alpha)
to the dual version of N=1 supergravity (e_m{}^a, \psi_m{}^\alpha, M_{m_1...
m_6}, \chi_\a,\Phi) in ten-dimensions. Our new 7-form field C has its 8-form
field strength H dual to the 2-form field strength F of the conventional vector
multiplet. We have found that the H-Bianchi identity must have the form N\wedge
F, where N is the 7-form field strength in dual supergravity. We also see why
only the dual version of supergravity couples to the dual vector multiplet
consistently. The potential anomaly for the dual vector multiplet can be
cancelled for the particular gauge group U(1)^{496} by the Green-Schwarz
mechanism. As a by-product, we also give the globally supersymmetric Abelian
Dirac-Born-Infeld interactions for the dual vector multiplet for the first
time.
