Of the trio of famous papers that Albert Einstein sent to the Annalen der Physik in 1905 only the paper proposing the photon concept has been unavailable in English translation. The American Journal of Physics is publishing the following translation in recognition of the sixtieth anniversary of the appearance of the original work. Physics teachers may take particular interest in the following aspects: (1) Einstein's keen awareness of the heuristic character of his new conception. (2) His demonstration from thermodynamic and statistical considerations that electromagnetic radiation might be conceived as consisting of finite numbers of discrete corpuscles of energy hv. (3) His prediction of the linear relation between the stopping potential of photoelectrons and the frequency of the incident light. This latter aspect of the photoelectric effect was not included among Lenard's early investigations. It remained for Millikan and others to develop the elegant experimental techniques that confirmed Einstein's bold prediction. Readers interested in pursuing the background in greater depth will find it rewarding to refer to the critical analyses by Martin J. Klein in "Einstein's First Paper on Quanta," in The Natural Philosopher (Blaisdell Publishing Company, New York, 1963), Vol. II, and "Einstein and the Wave-Particle Duality," in The Natural Philosopher, Vol. III, 1964. We are grateful to Professor Klein for his criticism and advice regarding this translation and for his generosity in making available to us an unpublished translation of his own.