We present six new transits of the hot Jupiter OGLE-TR-113b observed with MagIC on the Magellan Telescopes between January 2007 and May 2009 . We update the system parameters and revise the planetary radius to R _ { p } = 1.084 \pm 0.029 ~ { } R _ { 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 \pm 28 seconds over two years , placing an upper limit of 1 - 2 ~ { } M _ { \oplus } 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 \dot { P } = -60 \pm 15 milliseconds per year . If real , this change in period could result from either a long-period ( more than 8 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 .