  We construct a $p$-adic analog to AdS/CFT, where an unramified extension of
the $p$-adic numbers replaces Euclidean space as the boundary and a version of
the Bruhat-Tits tree replaces the bulk. Correlation functions are computed in
the simple case of a single massive scalar in the bulk, with results that are
strikingly similar to ordinary holographic correlation functions when expressed
in terms of local zeta functions. We give some brief discussion of the geometry
of $p$-adic chordal distance and of Wilson loops. Our presentation includes an
introduction to $p$-adic numbers.
