We report the detection of a faint old stellar system at ( \alpha, \delta ) = ( 194.29 ^ { \circ } ,~ { } 34.32 ^ { \circ } ) ( SDSS J1257+3419 ) , based on the spatial distribution of bright red-giant branch stars in the Sloan Digital Sky Survey Data Release 4 . SDSS J1257+3419 has a half-light radius of 38 \pm 12 pc and an absolute integrated V -magnitude of M _ { V } = -4.8 ^ { +1.4 } _ { -1.0 } mag at a heliocentric distance of 150 \pm 15 kpc . A comparison between SDSS J1257+3419 and known Galactic halo objects suggests that SDSS J1257+3419 is either ( a ) a faint and small dwarf galaxy or ( b ) a faint and widely extended globular cluster . In the former case , SDSS J1257+3419 could represent an entity of a postulated subhalo of the Milky Way . Further photometric and dynamical study of this stellar system is vital to discriminate these possibilities .