The paper considers the problem of computing a maximal independent set in hypergraphs (see [Karp, Ramachandran 88] and [Beame, Luby 89]). We present an efficient deterministic parallel algorithm for the case when the maximal cardinality of any hyperedge is 3. The algorithm works in $O(\log^4 n)$ parallel time with $O(n+m)$ processors on a CREW PRAM and is optimal up to a polylogarithmic factor.