  Chiral algebras in the cohomology of the $\overline{Q}_+$ supercharge of
two-dimensional $\mathcal{N}=(0,2)$ theories on flat spacetime are discussed.
Using the supercurrent multiplet, we show that the answer is renormalization
group invariant for theories with an R-symmetry. For $\mathcal{N}=(0,2)$
Landau-Ginzburg models, the chiral algebra is determined by the operator
equations of motion, which preserve their classical form, and quantum
renormalization of composite operators. We study these theories and then
specialize to the $\mathcal{N}=(2,2)$ models and consider some examples.
