  We present the first constraints on the cross-correlation power spectrum of
HeII ($^{+}{\rm He}^3$) signal strength using the redshifted 8.67GHz hyperfine
transition between $z=2.9$ and $z=4.1$ and with interferometric data obtained
from the public archive of the Australia Telescope Compact Array. 210 hours of
observations of the primary calibrator source B1934-638 were extracted from
data obtained with the telescope from 2014--2021, and coherently combined in a
power spectrum pipeline to measure the HeII power across a range of spatial
scales, and at three redshifts that span the period of Helium reionization. Our
best limit places the brightness temperature fluctuation to be less than
557$\mu$K on spatial scales of 30 arcmin at $z=2.91$, and less than 755$\mu$K
on scales of 30 arcmin at $z=4.14$ (2-sigma noise-limited). We measure a
temperature of 489$\mu$K at $z=2.91$. ATCA's few antennas and persistent
remaining RFI in the data prevent deeper integrations improving the results.
This work is a proof of principle to demonstrate how this type of experiment
can be undertaken to reach the 0.01--1$\mu$K level expected for the Helium
signal at $z \sim 4$.
