  We construct a locally supersymmetric worldsheet formulation of a non-Abelian
Ramond-Neveu-Schwarz (NARNS) string theory where the string coordinates are
noncommuting matrices in a group U(N). This is described by the two dimensional
supergravity coupled to supersymmetric Yang-Mills fields and adjoint matters in
the gauge group U(N). We show that our NARNS string theory has a free string
limit where it becomes N-copies of usual RNS string which can be described by
the orbifold conformal field theory corresponding to the covariant worldsheet
version of the Matrix string theory of Dijkgraaf, Verlinde and Verlinde. In the
weak coupling limit, i.e. $g_s \to 0$ where $g_s$ is the coupling constant of
our theory related with the Yang-Mills coupling as $g_{YM}^{-2}=\alpha' g_s^2$,
a new additional dimension appears in the string spectrum and it can be
speculatively interpreted as the compactified eleven dimensional coordinate
whose dynamics is given by an orbifold O(N) sigma model.
