We study the spectrum of W3 strings. In particular, we show that for
appropriately chosen space-time signature, one of the scalar fields is singled
out by the spin-3 constraint and is ``frozen'': no creation operators from it
can appear in physical states and the corresponding momentum must assume a
specific fixed value. The remaining theory is unitary and resembles an ordinary
string theory in d=26 with anomalies cancelled by appropriate background
charges. In the case of the W3 string, however, the spin-two ``graviton'' is
massive.Comment: 14 Page