We consider complete (possibly non-compact) three dimensional Riemannian manifolds
(M,g) such that: a) (M,g) is non-collapsed, b) the Ricci curvature of (M,g) is bounded
from below, c) the geometry of (M,g) at infinity is not too extreme. Given such initial
data (M,g) we show that a Ricci flow exists for a short time interval. This enables
us to construct a Ricci flow of any (possibly singular) metric space (X,d) which arises
as a Gromov-Hausdorff limit of a sequence of 3-manifolds which satisfy a), b) and
c) uniformly. As a corollary we show that such an X must be a manifold.