  Since the advent of inflation, several theorems have been proven suggesting
that although inflation can (and generically does) continue eternally into the
future, it cannot be extended eternally into the past to create a
``steady-state'' model with no initial time. Here we provide a construction
that circumvents these theorems and allows a self-consistent, geodesically
complete, and physically sensible steady-state eternally inflating universe,
based on the flat slicing of de Sitter space. This construction could be used
as the background space-time for creation events that form big-bang-like
regions, and hence could form the basis for a cosmology that is compatible with
observations and yet which avoids an initial singularity or beginning of time.
