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 .