  Cosmological phase transitions in the primordial universe can produce
anisotropic stochastic gravitational wave backgrounds (GWB), similar to the
cosmic microwave background (CMB). For adiabatic perturbations, the
fluctuations in GWB follow those in the CMB, but if primordial fluctuations
carry an isocurvature component, this need no longer be true. It is shown that
in non-minimal inflationary and reheating settings, primordial isocurvature can
survive in GWB and exhibit significant non-Gaussianity (NG) in contrast to the
CMB, while obeying current observational bounds. While probing such NG GWB is
at best a marginal possibility at LISA, there is much greater scope at future
proposed detectors such as DECIGO and BBO. It is even possible that the first
observations of inflation-era NG could be made with gravitational wave
detectors as opposed to the CMB or Large-Scale Structure surveys.
