  Let $G$ be a group, and $S$ a non-empty subset of $G$. Then $S$ is
\emph{product-free} if $ab\notin S$ for all $a, b \in S$. We say $S$ is
\emph{locally maximal product-free} if $S$ is product-free and not properly
contained in any other product-free set. A natural question is what is the
smallest possible size of a locally maximal product-free set in $G$. The groups
containing locally maximal product-free sets of sizes $1$ and $2$ were
classified by Giudici and Hart in 2009. In this paper, we prove a conjecture of
Giudici and Hart by showing that if $S$ is a locally maximal product-free set
of size $3$ in a group $G$, then $|G| \leq 24$. This allows us to complete the
classification of locally maximal product free sets of size 3.
