  We present the discovery of CWISE J050626.96$+$073842.4 (CWISE J0506$+$0738),
an L/T transition dwarf with extremely red near-infrared colors discovered
through the Backyard Worlds: Planet 9 citizen science project. Photometry from
UKIRT and CatWISE give a $(J-K)_{\rm MKO}$ color of 2.97$\pm$0.03 mag and a
$J_{\rm MKO}-$W2 color of 4.93$\pm$0.02 mag, making CWISE J0506$+$0738 the
reddest known free-floating L/T dwarf in both colors. We confirm the extremely
red nature of CWISE J0506$+$0738 using Keck/NIRES near-infrared spectroscopy
and establish that it is a low-gravity late-type L/T transition dwarf. The
spectrum of CWISE J0506$+$0738 shows possible signatures of CH$_4$ absorption
in its atmosphere, suggesting a colder effective temperature than other known,
young, red L dwarfs. We assign a preliminary spectral type for this source of
L8$\gamma$-T0$\gamma$. We tentatively find that CWISE J0506$+$0738 is variable
at 3-5 $\mu$m based on multi-epoch WISE photometry. Proper motions derived from
follow-up UKIRT observations combined with a radial velocity from our
Keck/NIRES spectrum and a photometric distance estimate indicate a strong
membership probability in the $\beta$ Pic moving group. A future parallax
measurement will help to establish a more definitive moving group membership
for this unusual object.
