Mars Orbiter Laser Altimeter (MOLA) data provide compelling evidence that the martian lowlands, below the smooth and sparsely cratered northern plains, are extremely old, far older than the plains which cover them. The evidence is in the form of a very large population of Quasi-Circular Depressions (QCDs), many of which are very evident in the MOLA elevation data but generally not visible in available imagery. We interpret these invisible QCDs to be buried impact basins. Cumulative number versus diameter curves for lowland QCDs suggests the buried lowland surface is older than the visible highland surface and that the lowland plains are a relatively thin (1--2 km) veneer overlying this much older surface. We conclude that the martian lowlands have been low and stable for nearly all of martian history.