An upper bound on the speed of evolution is derived. The bound concerns the amount of genetic information which is expressed in observable ways in various aspects of the phenotype. The genetic information expressed in some part of the phenotype of a species cannot increase faster than a given rate, determined by the selection pressure on that part. This rate is typically a small fraction of a bit per generation. Total expressed genetic information cannot increase faster than a species-specific rate--typically a few bits per generation. These bounds apply to all aspects of the phenotype, but are particularly relevant to cognition. As brains are highly complex, we expect large amounts of expressed genetic information in the brain--of the order of 100 kilobytes--yet evolutionary changes in brain genetic information are only a fraction of a bit per generation. This has important consequences for cognitive evolution. The limit implies that the human brain differs from the chimpanzee brain by at most 5 kilobytes of genetic design information. This is not enough to define a Language Acquisition Device, unless it depends heavily on pre-existing primate symbolic cognition. Subject to the evolutionary speed limit, in changing environments a simple, modular brain architecture is fitter than more complex ones. This encourages us to look for simplicity in brain design, rather than expecting the brain to be a patchwork of ad hoc adaptations. The limit implies that pure species selection is not an important mechanism of evolutionary change.