It is argued that the apparent constancy of the rate of molecular evolution may be an artifact due to the very slow rate of evolution of individual amino acids. A statistical analysis of protein evolution using a stationary point process as the null hypothesis leads to the conclusion that molecular evolution is episodic, with short bursts of rapid evolution followed by long periods of slow evolution. Such dynamics are incompatible with the neutral allele theory and require a revision of the standard interpretation of the molecular clock.