  The stochastic gravitational wave background (SGWB) contains a wealth of
information on astrophysical and cosmological processes. A major challenge of
upcoming years will be to extract the information contained in this background
and to disentangle the contributions of different sources. In this paper we
provide the formalism to extract, from the correlation of three signals in the
Laser Interferometer Space Antenna (LISA), information about the tensor
three-point function, which characterizes the non-Gaussian properties of the
SGWB. This observable can be crucial to discriminate whether a SGWB has a
primordial or astrophysical origin. Compared to the two-point function, the
SGWB three-point function has a richer dependence on the gravitational wave
momenta and chiralities. It can be used therefore as a powerful discriminator
between different models. For the first time we provide the response functions
of LISA to a general SGWB three-point function. As examples, we study in full
detail the cases of an equilateral and squeezed SGWB bispectra, and provide the
explicit form of the response functions, ready to be convoluted with any
theoretical prediction of the bispectrum to obtain the observable signal. We
further derive the optimal estimator to compute the signal-to-noise ratio. Our
formalism covers general shapes of non-Gaussianity, and can be extended
straightaway to other detector geometries. Finally, we provide a short overview
of models of the early universe that can give rise to a non-Gaussian SGWB.
