  We study matter-wave interferometry in the presence of a stochastic
background of gravitational waves. It is shown that if the background has a
scale-invariant spectrum over a wide bandwidth (which is expected in a class of
inflationary models of Big Bang cosmology), then separated-path interference
cannot be observed for a lump of matter of size above a limit which is very
insensitive to the strength and bandwidth of the fluctuations, unless the
interferometer is servo-controlled or otherwise protected. For ordinary solid
matter this limit is of order 1--10 mm. A servo-controlled or cross-correlated
device would also exhibit limits to the observation of macroscopic
interference, which we estimate for ordinary matter moving at speeds small
compared to c.
