  There is a global trend to increase the light yield of CsI scintillators used
in neutrino and dark matter detection by operating undoped crystals at
cryogenic temperatures. However, high light yield alone is not sufficient to
guarantee a low-energy threshold. The response of undoped crystals to nuclear
recoils at cryogenic temperatures is equally important. A liquid nitrogen-based
cryostat was developed to measure the nuclear quenching factor of a small
undoped CsI crystal using monoenergetic neutron beams at the Triangle
Universities Nuclear Laboratory (TUNL). To avoid neutron scattering in high-$Z$
materials, these materials were intentionally reduced around the crystal. The
structure and performance of the cryostat are described in detail. Using this
cryostat, a light yield of $33.4 \pm 1.7$ photoelectrons per keV
electron-equivalent (PE/keV$_\text{ee}$) was observed at 5.9 keV$_\text{ee}$,
enabling the measurement of nuclear quenching factors at very low energies. The
results of the quenching factor measurement will be reported in a subsequent
paper.
  Non-negligible negative overshoot was observed in the tails of the observed
light pulses. The origin of this issue and the correction procedure are
described in detail. This information may be useful for others who encounter
similar technical challenges.
