We present the discovery of CWISE J050626.96+073842.4 (CWISEJ0506+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)MKO color of 2.97+/-0.03mag and a J_MKO_-W2 color of 4.93+/-0.02mag, 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 CH4 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 multiepoch 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.