We present the first observation of Thomson-backscattered light from laser-accelerated electrons. In a compact, all-optical setup, the "photon collider," a high-intensity laser pulse is focused into a pulsed He gas jet and accelerates electrons to relativistic energies. A counterpropagating laser probe pulse is scattered from these high-energy electrons, and the backscattered x-ray photons are spectrally analyzed. This experiment demonstrates a novel source of directed ultrashort x-ray pulses and additionally allows for time-resolved spectroscopy of the laser acceleration of electrons.