We have prepared a degenerate gas of fermionic atoms which move in two
dimensions while the motion in the third dimension is "frozen" by tight
confinement and low temperature. {\it In situ} imaging provides direct
measurement of the density profile and temperature. The gas is confined in a
defect-free optical potential, and the interactions are widely tunable by means
of a Fano--Feshbach resonance. This system can be a starting point for
exploration of 2D Fermi physics and critical phenomena in a pure, controllable
environment