  We introduce a new integrable hierarchy of nonlinear differential-difference
equations which we call constrained Toda hierarchy (C-Toda). It can be regarded
as a certain subhierarchy of the 2D Toda lattice obtained by imposing the
constraint $\bar {\cal L}={\cal L}^{\dag}$ on the two Lax operators (in the
symmetric gauge). We prove the existence of the tau-function of the C-Toda
hierarchy and show that it is the square root of the 2D Toda lattice
tau-function. In this and some other respects the C-Toda is a Toda analogue of
the CKP hierarchy. It is also shown that zeros of the tau-function of elliptic
solutions satisfy the dynamical equations of the Ruijsenaars-Schneider model
restricted to turning points in the phase space. The spectral curve has
holomorphic involution which interchange the marked points in which the
Baker-Akhiezer function has essential singularities.
