We construct representations of the deformed Shatashvili–Vafa vertex algebra SVa, with parameter a ∈ ℂ, as recently proposed in the physics literature by Fiset and Gaberdiel. The geometric input for our construction are integrable G2-structures with closed torsion, solving the heterotic G2 system with α′ = 0 on the group manifolds S3 × T4 and S3 × S3 × S1. From considerations in string theory, one expects the chiral algebra of these backgrounds to include SVa, and we provide a mathematical realization of this expectation by obtaining embeddings of SVa in the corresponding superaffine vertex algebra and the chiral de Rham complex. In our examples, the parameter a is proportional to the scalar torsion class of the G2 structure, a ∼ τ0, as expected from previous work in the semi-classical limit by the second author, jointly with de la Ossa and Marchetto.