The paper considers the problem of computing a maximal independent set in a hypergraph (see \cite{BL} and \cite{KR}). We present an efficient deterministic NC algorithm for finding a maximal independent set in a hypergraph of dimension $3$: the algorithm runs in time $O(\log^4 n)$ time on $n+m$ processors of an EREW PRAM and is optimal up to a polylogarithmic factor. Our algorithm adapts the technique of Goldberg and Spencer (\cite{GS}) for finding a maximal independent set in a graph (or hypergraph of dimension $2$). It is the first NC algorithm for finding a maximal independent set in a hypergraph of dimension greater than 2.