Let R be a complete rank-1 valuation ring of mixed characteristic (0,p), and
let K be its field of fractions. A g-dimensional truncated Barsotti-Tate group
G of level n over R is said to have a level-n canonical subgroup if there is a
K-subgroup of G\tensor_R K with geometric structure (\Z/p^n\Z)^g consisting of
points "closest to zero". We give a nontrivial condition on the Hasse invariant
of G that guarantees the existence of the canonical subgroup, analogous to a
result of Katz and Lubin for elliptic curves. The bound is independent of the
height and dimension of G.