A left-invariant Lorentz structure on \(G=\mathrm{Aff}_+({\mathbb R})=\left\{(x,y)\colon y>0\right\}\) is a nondegenerate quadratic form of index \((1,1)\) on the Lie algebra \(\mathfrak{g}\). This note gives an expression for its Levi-Civita connection and states (without proof) that it always has constant sectional curvature, hence is locally isometric to either de Sitter space, Minkowski space or anti-de Sitter space. Further it describes its Lie algebra of Killing vector fields.