  Let $G$ be a locally compact group with left regular representation
$\lambda_{G}.$ We say that $G$ admits a frame of translates if there exist a
countable set $\Gamma\subset G$ and $\varphi\in L^{2}(G)$ such that
$(\lambda_{G}(x) \varphi)_{x \in\Gamma}$ is a frame for $L^{2}(G).$ The present
work aims to characterize locally compact groups having frames of translates,
and to this end, we derive necessary and/or sufficient conditions for the
existence of such frames. Additionally, we exhibit surprisingly large classes
of Lie groups admitting frames of translates.
