  The Universe may harbor relics of the post-inflationary epoch in the form of
a network of self-ordered scalar fields. Such fossils, while consistent with
current cosmological data at trace levels, may leave too weak an imprint on the
cosmic microwave background and the large-scale distribution of matter to allow
for direct detection. The non-Gaussian statistics of the density perturbations
induced by these fields, however, permit a direct means to probe for these
relics. Here we calculate the bispectrum that arises in models of self-ordered
scalar fields. We find a compact analytic expression for the bispectrum,
evaluate it numerically, and provide a simple approximation that may be useful
for data analysis. The bispectrum is largest for triangles that are aligned
(have edges $k_1\simeq 2 k_2 \simeq 2 k_3$) as opposed to the local-model
bispectrum, which peaks for squeezed triangles ($k_1\simeq k_2 \gg k_3$), and
the equilateral bispectrum, which peaks at $k_1\simeq k_2 \simeq k_3$. We
estimate that this non-Gaussianity should be detectable by the Planck satellite
if the contribution from self-ordering scalar fields to primordial
perturbations is near the current upper limit.
