We report the discovery of KELT-10b, the first transiting exoplanet discovered using the KELT-South telescope. KELT-10b is a highly inflated sub-Jupiter mass planet transiting a relatively bright V = 10.7 star (TYC 8378-64-1), with T eff = 5948 ± 74 K, log g = 4.319 +0.020 −0.030 and [Fe/H] = 0.09 +0.11 −0.10 , an inferred mass M * = 1.112 +0.055 −0.061 M and radius R * = 1.209 +0.047 −0.035 R . The planet has a radius R p = 1.399 +0.069 −0.049 R J and mass M p = 0.679 +0.039 −0.038 M J . The planet has an eccentricity consistent with zero and a semi-major axis a = 0.05250 +0.00086 −0.00097 AU. The best fitting linear ephemeris is T 0 = 2457066.72045±0.00027 BJD TDB and P = 4.1662739±0.0000063 days. This planet joins a group of highly inflated transiting exoplanets with a radius larger and a mass less than that of Jupiter. The planet, which boasts deep transits of 1.4%, has a relatively high equilibrium temperature of T eq = 1377 +28 −23 K, assuming zero albedo and perfect heat redistribution. KELT-10b receives an estimated insolation of 0.817 +0.068 −0.054 × 10 9 erg s −1 cm −2 , which places it far above the insolation threshold above which hot Jupiters exhibit increasing amounts of radius inflation. Evolutionary analysis of the host star suggests that KELT-10b may not survive beyond the current subgiant phase, depending on the rate of in-spiral of the planet over the next few Gyr. The planet transits a relatively bright star and exhibits the third largest transit depth of all transiting exoplanets with V < 11 in the southern hemisphere, making it a promising candidate for future atmospheric characterization studies.