  Let $R$ be any ring with identity and Ch($R$) the category of chain complexes
of (left) $R$-modules. We show that the Gorenstein AC-projective chain
complexes are the cofibrant objects of an abelian model structure on Ch($R$).
The model structure is cofibrantly generated and is projective in the sense
that the trivially cofibrant objects are the categorically projective chain
complexes. We show that when $R$ is a Ding-Chen ring, that is, a two-sided
coherent ring with finite self FP-injective dimension, then the model structure
is finitely generated, and so its homotopy category is compactly generated.
Constructing this model structure also shows that every chain complex over any
ring has a Gorenstein AC-projective precover. These are precisely Gorenstein
projective (in the usual sense) precovers whenever $R$ is either a Ding-Chen
ring, or, a ring for which all level (left) $R$-modules have finite projective
dimension. For a general (right) coherent ring $R$, the Gorenstein
AC-projective complexes coincide with the Ding projective complexes and so
provide such precovers in this case.
