The brightness of type Ia supernovae, and their homogeneity as a class, makes them powerful tools in cosmology, yet little is known about the progenitor systems of these explosions. They are thought to arise when a white dwarf accretes matter from a companion star, is compressed and undergoes a thermonuclear explosion. Unless the companion star is another white dwarf (in which case it should be destroyed by the mass-transfer process itself), it should survive and show distinguishing properties. Tycho's supernova is one of only two type Ia supernovae observed in our Galaxy, and so provides an opportunity to address observationally the identification of the surviving companion. Here we report a survey of the central region of its remnant, around the position of the explosion, which excludes red giants as the mass donor of the exploding white dwarf. We found a type G0-G2 star, similar to our Sun in surface temperature and luminosity (but lower surface gravity), moving at more than three times the mean velocity of the stars at that distance, which appears to be the surviving companion of the supernova.