Rolling tachyon solution of two-dimensional string theory

We consider a classical (string) field theory of c = 1 matrix model which was developed earlier in hep-th/9207011 and subsequent papers. This is a noncommutative field theory where the noncommutativity parameter is the string coupling gs. We construct a classical solution of this field theory and show that it describes the complete time history of the recently found rolling tachyon on an unstable D0 brane. (author)