  We consider the 3-pt function (i.e. the bispectrum or non-Gaussianity) for
stochastic backgrounds of gravitational waves. We estimate the amplitude of
this signal for the primordial inflationary background, gravitational waves
generated during preheating, and for gravitational waves produced by
self-ordering scalar fields following a global phase transition. To assess
detectability, we describe how to extract the 3-pt signal from an idealized
interferometric experiment and compute the signal to noise ratio as a function
of integration time. The 3-pt signal for the stochastic gravitational wave
background generated by inflation is unsurprisingly tiny. For gravitational
radiation generated by purely causal, classical mechanisms we find that, no
matter how non-linear the process is, the 3-pt correlations produced vanish in
direct detection experiments. On the other hand, we show that in scenarios
where the B-mode of the CMB is sourced by gravitational waves generated by a
global phase transition, a strong 3-pt signal among the polarization modes
could also be produced. This may provide another method of distinguishing
inflationary B-modes. To carry out this computation, we have developed a
diagrammatic approach to the calculation of stochastic gravitational waves
sourced by scalar fluids, which has applications beyond the present scenario.
