  We construct a cofibrantly generated model structure on the category of
differential non-negatively graded quasi-coherent commutative $D_X$-algebras,
where $D_X$ is the sheaf of differential operators of a smooth afine algebraic
variety X. The paper contains an extensive appendix on D-modules, sheaves
versus global sections, some more technical model categorical issues, as well
as on relative Sullivan algebras. This article is the first of a series of
works -located at the interface of homotopical algebra, algebraic geometry, and
mathematical physics - on a derived D-geometric approach to the BV-formalism.
