  We report deep, single-dish 21 cm observations of NGC 1052-DF2, taken with
the Green Bank Telescope. NGC 1052-DF2, proposed to be lacking in dark matter,
is currently classified as an ultra-diffuse galaxy in the NGC 1052 group. We do
not detect the galaxy, and derive an upper limit on the HI, mass. The galaxy is
extremely gas-poor, and we find that a $3\sigma \, M_{HI}$ detection at a
distance of 19 Mpc and using a line width of 3.2 km $\rm s^{-1}$ would have an
upper limit of $M_{HI,lim} < 5.5 \times 10^5$ M$_{\odot}$. At this mass limit,
the gas fraction of neutral gas mass to stellar mass is extremely low, at
$M_{HI}$/M$_{*}$ $\, < \, 0.0027$. This extremely low gas fraction, comparable
to Galactic dwarf spheroidals and gas-poor dwarf ellipticals, implies that
either the galaxy is within the virial radius of NGC1052, where its gas has
been stripped due to its proximity to the central galaxy, or that NGC 1052-DF2
is at distance large enough to inhibit detection of its gas. We also estimated
the upper limit of the HI mass of NGC 1052-DF2 resided at 13 Mpc. This would
give an HI mass of $M_{HI,lim} < 2.5 \times 10^5$ M$_{\odot}$, and an HI gas
fraction of $M_{HI}$/M$_{*}$r $\, < \, 0.0012$, becoming even more extreme.
While the dark matter fraction would be less extreme at this distance, the
neutral gas fraction would be unprecedented for an object in a low density
environment.
