  Let $H$ be a $k$-uniform hypergraph with $n$ vertices. A {\em strong
$r$-coloring} is a partition of the vertices into $r$ parts, such that each
edge of $H$ intersects each part. A strong $r$-coloring is called {\em
equitable} if the size of each part is $\lceil n/r \rceil$ or $\lfloor n/r
\rfloor$. We prove that for all $a \geq 1$, if the maximum degree of $H$
satisfies $\Delta(H) \leq k^a$ then $H$ has an equitable coloring with
$\frac{k}{a \ln k}(1-o_k(1))$ parts. In particular, every $k$-uniform
hypergraph with maximum degree $O(k)$ has an equitable coloring with
$\frac{k}{\ln k}(1-o_k(1))$ parts. The result is asymptotically tight. The
proof uses a double application of the non-symmetric version of the Lov\'asz
Local Lemma.
