We present seven light curves of the exoplanet system HAT-P-3, taken as part of a transit timing program using the RISE instrument on the Liverpool Telescope. The light curves are analysed using a Markov-Chain Monte-Carlo algorithm to update the parameters of the system. The inclination is found to be i = 86.75^{+0.22}_{-0.21} deg, the planet-star radius ratio to be R_p/R_star = 0.1098^{+0.0010}_{-0.0012}, and the stellar radius to be R_star = 0.834^{+0.018}_{-0.026} R_sun, consistent with previous results but with a significant improvement in the precision. Central transit times and uncertainties for each light curve are also determined, and a residual permutation algorithm used as an independent check on the errors. The transit times are found to be consistent with a linear ephemeris, and a new ephemeris is calculated as T_c(0) = 2454856.70118 +- 0.00018 HJD and P = 2.899738 +- 0.000007 days. Model timing residuals are fitted to the measured timing residuals to place upper mass limits for a hypothetical perturbing planet as a function of the period ratio. These show that we have probed for planets with masses as low as 0.33 M_earth and 1.81 M_earth in the interior and exterior 2:1 resonances, respectively, assuming the planets are initially in circular orbits.
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