  We provide an efficient algorithm for the classical problem, going back to
Galton, Pearson, and Fisher, of estimating, with arbitrary accuracy the
parameters of a multivariate normal distribution from truncated samples.
Truncated samples from a $d$-variate normal ${\cal
N}(\mathbf{\mu},\mathbf{\Sigma})$ means a samples is only revealed if it falls
in some subset $S \subseteq \mathbb{R}^d$; otherwise the samples are hidden and
their count in proportion to the revealed samples is also hidden. We show that
the mean $\mathbf{\mu}$ and covariance matrix $\mathbf{\Sigma}$ can be
estimated with arbitrary accuracy in polynomial-time, as long as we have oracle
access to $S$, and $S$ has non-trivial measure under the unknown $d$-variate
normal distribution. Additionally we show that without oracle access to $S$,
any non-trivial estimation is impossible.
