We present the discovery of a faint, resolved stellar system, BLISS J0321+0438 (BLISS 1), found in Dark Energy Camera data from the first observing run of the Blanco Imaging of the Southern Sky (BLISS) Survey. BLISS J0321+0438 (BLISS 1) is located at (α 2000 , δ 2000 ) = (177. • 511, −41. • 772) with a heliocentric distance of D = 23.7 +1.9 −1.0 kpc. It is a faint, M V = 0.0 +1.7 −0.7 mag, and compact, r h = 4.1 +1 −1 pc, system consistent with previously discovered faint halo star clusters. Using data from the second data release of the Gaia satellite, we measure a proper motion of (µ α cos δ, µ δ ) = (−2.37 ± 0.06, 0.16±0.04) mas/yr. Combining the available positional and velocity information with simulations of the accreted satellite population of the Large Magellanic Cloud (LMC), we find that it is unlikely that BLISS J0321+0438 (BLISS 1) originated with the LMC.