  After adding a scalar chiral boson to the usual superspace variables, the
four-dimensional Green-Schwarz superstring is quantized in a manifestly SO(3,1)
super-Poincar\'e covariant manner. The constraints are all first-class and form
an N=2 superconformal algebra with $c=-3$. Since the Calabi-Yau degrees of
freedom are described by an N=2 superconformal field theory with $c=9$, the
combined Green-Schwarz and Calabi-Yau systems form the $c=6$ matter sector of a
critical N=2 string.
  Using the standard N=2 super-Virasoro ghosts, a nilpotent BRST charge is
defined and vertex operators for the massless supermultiplets are constructed.
Four-dimensional superstring amplitudes can be calculated with manifest SO(3,1)
super-Poincar\'e invariance by evaluating correlation functions of these
BRST-invariant vertex operators on N=2 super-Riemann surfaces.
