  Ancient solutions of the Ricci flow arise naturally as models for singularity
formation. There has been significant progress towards the classification of
such solutions under natural geometric assumptions. Nonnegatively curved
solutions in dimensions 2 and 3, and uniformly PIC solutions in higher
dimensions are now well understood. We consider ancient solutions of arbitrary
dimension which are complete and have Type~I curvature growth. We show that a
$\kappa$-noncollapsed Type~I ancient solution which is noncompact and has
nonnegative sectional curvature necessarily splits at least one Euclidean
factor. It follows that a $\kappa$-noncollapsed Type~I ancient solution which
is weakly PIC2 is a locally symmetric space.
