  We derive the low energy effective action of the heterotic superstring in
superspace. This is achieved by coupling the covariantly quantized
Green-Schwarz superstring of Berkovits to a curved background and requiring
that the sigma model has superconformal invariance at tree level and at one
loop in $\a'$. Tree level superconformal invariance yields the complete
supergravity algebra, and one-loop superconformal invariance the equations of
motion of the low energy theory. The resulting low energy theory is old-minimal
supergravity coupled to a tensor multiplet. The dilaton is part of the
compensator multiplet.
