  Parity violation is a powerful observable to distinguish a cosmological
background of Gravitational Waves (GWs) from an astrophysical one. Planar
single GW interferometers, both on ground and in space, are unable to measure
the net circular polarization of an isotropic Stochastic Gravitational Wave
Background (SGWB). In this paper, we explore the possibility of detecting
circular polarization of an isotropic SGWB by cross-correlating two space-based
detectors planned to be launched around 2034: LISA and Taiji. We compute the
response of such a network to chirality and we perform a Fisher forecast
analysis on the $I$ and $V$ Stokes parameters for the SGWB. We find that a
clear measurement of chirality can be claimed for a maximally chiral signal
with $h^2 \, \Omega_{\rm GW} \simeq 10^{-12}$.
