  We report the detection of 21 cm emission at an average redshift $\bar{z} =
2.3$ in the cross-correlation of data from the Canadian Hydrogen Intensity
Mapping Experiment (CHIME) with measurements of the Lyman-$\alpha$ forest from
eBOSS. Data collected by CHIME over 88 days in the $400-500$~MHz frequency band
($1.8 < z < 2.5$) are formed into maps of the sky and high-pass delay filtered
to suppress the foreground power, corresponding to removing cosmological scales
with $k_\parallel \lesssim 0.13\ \text{Mpc}^{-1}$ at the average redshift.
Line-of-sight spectra to the eBOSS background quasar locations are extracted
from the CHIME maps and combined with the Lyman-$\alpha$ forest flux
transmission spectra to estimate the 21 cm-Lyman-$\alpha$ cross-correlation
function. Fitting a simulation-derived template function to this measurement
results in a $9\sigma$ detection significance. The coherent accumulation of the
signal through cross-correlation is sufficient to enable a detection despite
excess variance from foreground residuals $\sim6-10$ times brighter than the
expected thermal noise level in the correlation function. These results are the
highest-redshift measurement of \tcm emission to date, and set the stage for
future 21 cm intensity mapping analyses at $z>1.8$.
