  In the pure spinor formalism for the superstring, the b-ghost is a composite
operator satisfying {Q,b}=T where Q is the pure spinor BRST operator and T is
the holomorphic stress tensor. The b-ghost is holomorphic in a flat
target-space background, but it is not holomorphic in a generic curved
target-space background and instead satisfies $\bar\partial b$ = [Q, \Omega]
for some \Omega. In this paper, \Omega\ is explicitly constructed for the case
of an open superstring in a super-Maxwell background.
