We present the discovery of a new dwarf galaxy, Perseus I/Andromeda XXXIII, found in the vicinity of Andromeda (M31) in stacked imaging data from the Pan-STARRS1 3π survey. Located 27fdg9 away from M31, Perseus I has a heliocentric distance of 785 ± 65 kpc, compatible with it being a satellite of M31 at 374−10+14kpc from its host. The properties of Perseus I are typical for a reasonably bright dwarf galaxy (MV = –10.3 ± 0.7), with an exponential half-light radius of rh = 1.7 ± 0.4 arcmin or rh=400−85+105pc at this distance, and a moderate ellipticity (ϵ=0.43−0.17+0.15). The late discovery of Perseus I is due to its fairly low surface brightness (μ0=25.7−0.9+1.0 mag arcsec–2), and to the previous lack of deep, high quality photometric data in this region. If confirmed to be a companion of M31, the location of Perseus I, far east from its host, could place interesting constraints on the bulk motion of the satellite system of M31.Astronom