Mapping spaces for chain complexes

Question

For any model category $M$, there is a mapping space $Map(X,Y)$ for two objects $X,Y$ of $M$ such that $\pi_0(Map(X,Y)) = Hom(X,Y)$ in $Ho(M)$. Chain complexes over a ring $R$ have a model structure (say the projective module structure). What is $Map(X,Y)$ for two chain complexes $X,Y$? For example, what are the higher homotopy groups of $Map(X,X)$ in terms of the chain complex $X$ when $R = \mathbb{Z}$?