We examine a stationary but non-static asymptotically AdS₃ spacetime with two causally connected conformal boundaries, each of which is a ``null cylinder'', namely a cylinder with a null direction identified. This spacetime arises from three different perspectives: (i) as a non-singular, causally regular orbifold of global AdS<sub>3</sub> by boosts, (ii) as a Penrose-like limit focusing on the horizon of extremal BTZ black holes, and (iii) as an S<sup>1</sup> fibration over AdS<sub>2</sub>. Each of these perspectives sheds an interesting light on holography. Examination of the conformal boundary of the spacetime shows that the dual to the space should involve DLCQ limits of the D1-D5 conformal field theory. The Penrose-like limit approach leads to a similar conclusion, by isolating a sector of the complete D1-D5 CFT that describes the physics in the vicinity of the horizon of an extremal black hole. As such this is a holographic description of the universal horizon dynamics of the extremal black holes in AdS<sub>3</sub> and also of the four and five dimensional stringy black holes whose states were counted in string theory. The AdS<sub>2</sub> perspective draws a connection to a 0+1d quantum mechanical theory. Various dualities lead to a Matrix model description of the spacetime. Many interesting issues that are related to both de Sitter physics and attempts to ``see behind a horizon'' using AdS/CFT arise from (a) the presence of two disconnected components to the boundary, and (b) the analytic structure of bulk physics in the complex coordinate plane.