given a finite-dimensional lie algebra $g$ and a $g$-module $v$, the ring $d(v)^g$ of invariant differential operators is a much-studied object in classical invariant theory. it has a natural vertex algebra analogue. first, $d(v)$ has a $va$ analogue $s(v)$ known as a $\beta\gamma$-system or algebra of chiral differential operators. the action of $g$ on $v$ induces an action of the corresponding affine algebra on $s(v)$. the invariant space $s(v)^{g[t]}$ is a commutant subalgebra of $s(v)$, and plays the role of $d(v)^g$. in this talk, i'll describe $s(v)^{g[t]}$ in some basic but nontrivial cases: when $g$ is abelian and the action is diagonalizable, and when $g$ is one of the classical lie algebras $sl(n), gl(n)$, or so$(n)$, and $v = c^n$. the answer is often a surprise: for example, when $g = c = v, s(v)^{g[t]}$ is the zamolodchikov $w_3$ algebra with central charge $c=-2$.