The detection and characterization of an Earth-like planet orbiting a nearby star requires a telescope with an extraordinarily large contrast at small angular separations. At visible wavelengths, an Earth-like planet would be 1 x 10(-10) times fainter than the star at angular separations of typically 0.1 arcsecond or less(1,2). There are several proposed space telescope systems that could, in principle, achieve this(3-6). Here we report a laboratory experiment that reaches these limits. We have suppressed the diffracted and scattered light near a star- like source to a level of 6 x 10(-10) times the peak intensity in individual coronagraph images. In a series of such images, together with simple image processing, we have effectively reduced this to a residual noise level of about 0.1 x 10(-10). This demonstrates that a coronagraphic telescope in space could detect and spectroscopically characterize nearby exoplanetary systems, with the sensitivity to image an ` Earth- twin' orbiting a nearby star.