If $G$ is a projective special linear group $\text{PSL}(3,q)$with$q \equiv 4 \; \text{or} \; 7 \pmod{9}$, then a Sylow 3-subgroup of $G$ iselementary abelianof order 9.We showthat the principal 3-blocks of any two such groups are Morita equivalent.This result and Okuyama's theorem for $\text{PSL}(3,4)$ provethe Broué conjecture for these blocks. 1991 Mathematics Subject Classification: 20C05, 20C20.