  For a set of positive integers $A \subseteq [n]$, an $r$-coloring of $A$ is
rainbow sum-free if it contains no rainbow Schur triple. In this paper we
initiate the study of the rainbow Erd\H{o}s-Rothchild problem in the context of
sum-free sets, which asks for the subsets of $[n]$ with the maximum number of
rainbow sum-free $r$-colorings. We show that for $r=3$, the interval $[n]$ is
optimal, while for $r\geq8$, the set $[\lfloor n/2 \rfloor, n]$ is optimal. We
also prove a stability theorem for $r\geq4$. The proofs rely on the hypergraph
container method, and some ad-hoc stability analysis.
