We present the discovery of an extremely cold, nearby brown dwarf in the solar neighborhood, found in the CatWISE catalog (Eisenhardt et al., in prep.). Photometric follow-up with Spitzer reveals that the object, CWISEP J193518.59-154620.3, has ch1$-$ch2 = 3.24$,pm,$0.31 mag, making it one of the reddest brown dwarfs known. Using the Spitzer photometry and the polynomial relations from Kirkpatrick et al. (2019) we estimate an effective temperature in the $sim$270--360 K range, and a distance estimate in the 5.6$-$10.9 pc range. We combined the WISE, NEOWISE, and Spitzer data to measure a proper motion of $mu_alpha cos delta = 337pm69$ mas yr$^{-1}$, $mu_delta = -50pm97$ mas yr$^{-1}$, which implies a relatively low tangential velocity in the range 7$-$22 km s$^{-1}$.