We have made a comprehensive transit search for exoplanets down to \simeq 1.5 - 2 Earth radii in the HD 189733 system , based on 21-days of nearly uninterrupted broadband optical photometry obtained with the MOST ( Microvariability & Oscillations of STars ) satellite in 2006 . We have searched these data for realistic limb-darkened transits from exoplanets other than the known hot Jupiter , HD 189733b , with periods ranging from about 0.4 days to one week . Monte Carlo statistical tests of the data with synthetic transits inserted into the data-set allow us to rule out additional close-in exoplanets with sizes ranging from about 0.15 - 0.31 R _ { J } ( Jupiter radii ) , or 1.7 - 3.5 R _ { \earth } ( Earth radii ) on orbits whose planes are near that of HD 189733b . These null results constrain theories that invoke lower-mass hot Super-Earth and hot Neptune planets in orbits similar to HD 189733b due to the inward migration of this hot Jupiter . This work also illustrates the feasibility of discovering smaller transiting planets around chromospherically active stars .