  The general form of a 2D conformal field theory (CFT) correlator on a
Euclidean Riemann surface, Lorentzian plane or Lorentzian cylinder is
well-known. This paper describes the general form of 2- and 3-point CFT
correlators on the Lorentzian torus $\mathcal{LT}^2$ which arises as the
conformal boundary of the group manifold $\mathrm{SL}(2,\mathbb{R})$ $\simeq
\text{AdS}_3/\mathbb{Z}$. We consider only generic points, thereby omitting an
analysis of contact terms, which already exhibits a surprisingly rich
structure. The results are relevant to celestial holography, for which the
$\mathcal{LT}^2$ at the boundary of Klein space is the home of the putative
celestial CFT.
