The LZ2 compression method seems hardly parallelizable since some related heuristics are known to be P-complete. In spite of such negative result, the decoding process can be parallelized efficiently.In this paper, we show a work-optimal parallel decoding Las Vegas algorithm for text compressed by a standard implementation of the LZ2 algorithm (next character heuristic). The algorithm works in expected logarithmic time on a PRAM CRCW.We also address a different implementation called identity heuristic. In this case, we need to make the realistic assumption that the length of the dictionary elements is logarithmic in order to decode with optimal parallel work. The algorithm takes deterministic logarithmic time on a PRAM CREW.