We report a random delayed-choice quantum eraser experiment. In a Young's double-slit interferometer, the which-slit information is learned from the photon-number fluctuation correlation of thermal light. The reappeared interference indicates that the which-slit information of a photon, or wave packet, can be "erased" by a second photon or wave packet, even after the annihilation of the first. Different from an entangled photon pair, the jointly measured two photons, or wave packets, are just two randomly distributed and randomly created photons of a thermal source that fall into the coincidence time window. The experimental observation can be explained as a nonlocal interference phenomenon in which a random photon or wave packet pair, interferes with the pair itself at distance.