We present six new transits of the hot Jupiter OGLE-TR-113b observed with MagIC on the Magellan Telescopes between 2007 January and 2009 May. We update the system parameters and revise the planetary radius to R{sub p} = 1.084 {+-} 0.029R{sub J} , where the error is dominated by stellar radius uncertainties. The new transit midtimes reveal no transit timing variations from a constant ephemeris of greater than 13 {+-} 28 s over two years, placing an upper limit of 1-2 M{sub +} on the mass of any perturber in a 1:2 or 2:1 mean-motion resonance with OGLE-TR-113b. Combining the new transit epochs with five epochs published between 2002 and 2006, we find hints that the orbital period of the planet may not be constant, with the best fit indicating a decrease of P-dot =-60{+-}15 ms yr{sup -1}. If real, this change in period could result from either a long-period (more than eight years) timing variation due to a massive external perturber or more intriguingly from the orbital decay of the planet. The detection of a changing period is still tentative and requires additional observations, but if confirmed it would enable direct tests of tidal stability and dynamical models of close-in planets.