  For a digraph $G$ and $v \in V(G)$, let $\delta^+(v)$ be the number of
out-neighbors of $v$ in $G$. The Caccetta-H\"{a}ggkvist conjecture states that
for all $k \ge 1$, if $G$ is a digraph with $n = |V(G)|$ such that $\delta^+(v)
\ge k$ for all $v \in V(G)$, then G contains a directed cycle of length at most
$\lceil n/k \rceil$. In [2], Aharoni proposes a generalization of this
conjecture, that a simple edge-colored graph on $n$ vertices with $n$ color
classes, each of size $k$, has a rainbow cycle of length at most $\lceil n/k
\rceil$. In this paper, we prove this conjecture if each color class has size
${\Omega}(k \log k)$.
