We present the discovery of KELT-1b, the first transiting low-mass companion from the wide-field Kilodegree Extremely Little Telescope-North (KELT-North) transit survey. A joint analysis of the spectroscopic, radial velocity, and photometric data indicates that the V = 10.7 primary is a mildly evolved mid-F star with T sub(eff) = 6516+ or -49 K, log g = 4.228 super(+0.014) sub(-0.021) , and Fe/H = 0.052+ or -0.079, with an inferred mass M sub(*) = 1.335 + or - 0.063 M sub(middot in circle) and radius R sub(*) = 1.471 super(+0.045) sub(0.035) R sub(middot in circle). The companion is a low-mass brown dwarf or a super-massive planet with mass M sub(p) = 27.38 + or - 0.93 M sub(Jup) and radius R sub(p) = 1.116 super(+0.038) sub(-0.029) R sub(Jup). Comparison with standard evolutionary models suggests that the radius of KELT-1b is likely to be significantly inflated. Adaptive optics imaging reveals a candidate stellar companion to KELT-1 with a separation of 588 + or - 1 mas, which is consistent with an M dwarf if it is at the same distance as the primary.