  The noncritical $4D$ $\cW_3$ string is a model of $\cW_3$ gravity coupled to
two free scalar fields. In this paper we discuss its BRST quantization in
direct analogy with that of the $2D$ (Virasoro) string. The physical operators
form a BV-algebra. We model this BV-algebra on that of the polyderivations of a
commutative ring on six variables with a quadratic constraint, or,
equivalently, on the BV-algebra of (polynomial) polyvector fields on the base
affine space of $SL(3,\CC)$. Details have appeared elsewhere. To appear in the
proceedings of ``STRINGS '95: Future Perspectives in String Theory,'' USC,
March 13--18, 1995
