Quantum BV ${\mathcal{L}}_{\mathrm{\infty }}$-algebras I: Derived geometric foundations

We introduce the concept of a quantum BV ${\mathcal{L}}_{\mathrm{\infty }}$-algebra and study fundamental properties. In particular, we investigate homotopy Lie theoretic structures that naturally arise in the context of Chern-Simons theory. Of note, are the notions of homotopy BV data and of a BV orientation. The sequel of this paper will involve the direct application of these constructions to the setting of Chern-Simons theory.