  We estimate the gravitational radiation signature of the electron/positron
annihilation-driven neutrino burst accompanying the asymmetric collapse of an
initially hydrostatic, radiation-dominated supermassive object suffering the
Feynman-Chandrasekhar instability. An object with a mass
$5\times10^4\,M_\odot<M<5\times10^5\,M_\odot$, with primordial metallicity, is
an optimal case with respect to the fraction of its rest mass emitted in
neutrinos as it collapses to a black hole: lower initial mass objects will be
subject to scattering-induced neutrino trapping and consequently lower
efficiency in this mode of gravitational radiation generation; while higher
masses will not get hot enough to radiate significant neutrino energy before
producing a black hole. The optimal case collapse will radiate several percent
of the star's rest mass in neutrinos and, with an assumed small asymmetry in
temperature at peak neutrino production, produces a characteristic linear
memory gravitational wave burst signature. The timescale for this signature,
depending on redshift, is $\sim1{\rm~s}$ to $10{\rm~s}$, optimal for proposed
gravitational wave observatories like DECIGO. Using the response of that
detector, and requiring a signal-to-noise ratio SNR $>$ 5, we estimate that
collapse of a $\sim 5\times10^4\,M_\odot$ supermassive star could produce a
neutrino burst-generated gravitational radiation signature detectable to
redshift $z\lesssim7$. With the envisioned ultimate DECIGO design sensitivity,
we estimate that the linear memory signal from these events could be detectable
with SNR $> 5$ to $z \lesssim13$.
