  We prove that a class of solutions to Einstein's equations---originally
discovered by G. C. McVittie in 1933---includes regular black holes embedded in
Friedman-Robertson-Walker cosmologies. If the cosmology is dominated at late
times by a positive cosmological constant, the metric is regular everywhere on
and outside the black hole horizon and away from the big bang singularity, and
the solutions asymptote in the future and near the horizon to the
Schwarzschild-de Sitter geometry. For solutions without a positive cosmological
constant the would-be horizon is a weak null singularity.
