  Let $H$ be a triple system with maximum degree $d>1$ and let
$r>10^7\sqrt{d}\log^{2}d$. Then $H$ has a proper vertex coloring with $r$
colors such that any two color classes differ in size by at most one. The bound
on $r$ is sharp in order of magnitude apart from the logarithmic factors.
Moreover, such an $r$-coloring can be found via a randomized algorithm whose
expected running time is polynomial in the number of vertices of $\cH$.
  This is the first result in the direction of generalizing the
Hajnal-Szemer\'edi theorem to hypergraphs.
