  We introduce a $Q$-operator $\mathcal{Q}_z$ for the hyperbolic
Calogero--Moser system as a one-parameter family of explicit integral
operators. We establish the standard properties of a $Q$-operator,
i.e.~invariance of Hamiltonians, commutativity for different parameter values
and that its eigenvalues satisfy an explicitly given first order ordinary
difference equation in the parameter $z$.
