  In this work, we present a method for implementing the $\delta N$ formalism
to study the primordial non-Gaussianity produced in multiple three-form field
inflation. Using a dual description relating three-form fields to noncanonical
scalar fields, and employing existing results, we produce expressions for the
bispectrum of the curvature perturbation in terms of three-form quantities. We
study the bispectrum generated in a two three-form field inflationary scenario
for a particular potential that for suitable values of the parameters was found
in earlier work to give values of the spectral index and ratio of tensor to
scalar perturbations compatible with current bounds. We calculate the reduced
bispectrum for this model, finding an amplitude in equilateral and orthogonal
configurations of ${\cal O}(1)$ and in the squeezed limit of ${\cal
O}(10^{-3})$. We confirm, therefore, that this three-form inflationary scenario
is compatible with present observational constraints.
