We have measured transit times for HD 189733b passing in front of its bright (V = 7.67) chromospherically active and spotted parent star. Nearly continuous broadband optical photometry of this system was obtained with the MOST (Microvariability & Oscillations of STars) space telescope during 21 days in August 2006, monitoring 10 consecutive transits. We have used these data to search for deviations from a constant orbital period which can indicate the presence of additional planets in the system that are as yet undetected by Doppler searches. There are no transit timing variations above the level of ${pm}45$ s, ruling out super-Earths (of masses $1 - 4 M_{earth}$) in the 1:2 and 2:3 inner resonances and planets of 20 $M_{earth}$ in the 2:1 outer resonance of the known planet. We also discuss complications in measuring transit times for a planet that transits an active star with large star spots, and how the transits can help constrain and test spot models. This has implications for the large number of such systems expected to be discovered by the CoRoT and Kepler missions.
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