  We construct black hole solutions to Einstein-Born-Infeld gravity with a
cosmological constant. Since an elliptic function appears in the solutions for
the metric, we construct horizons numerically. The causal structure of these
solutions differ drastically from their counterparts in Einstein-Maxwell
gravity with a cosmological constant. The charged de-Sitter black holes can
have up to three horizons and the charged anti-de Sitter black hole can have
one or two depending on the parameters chosen.
