We report the discovery of a bright transient X-ray source, CXOU J132518.2-430304, toward Centaurus A (Cen A) using six new Chandra X-Ray Observatory observations in 2007 March-May. Between 2003 and 2007, its flux has increased by a factor of >770. The source is likely a low-mass X-ray binary in Cen A with unabsorbed 0.3-10 keV band luminosities of (2-3) × 10 39ergs s-1 and a transition from the steep-power-law state to the thermal state during our observations. CXOU J132518.2-430304 is the most luminous X-ray source in an early-type galaxy with extensive timing information that reveals transience and a spectral state transition. Combined with its luminosity, these properties make this source one of the strongest candidates to date for containing a stellar-mass black hole in an early-type galaxy. Unless this outburst lasts many years, the rate of luminous transients in Cen A is anomalously high compared to other early-type galaxies.