  This article classifies closed G2-structures such that the induced metric is
conformally flat. It is shown that any closed G2-structure with conformally
flat metric is locally equivalent to one of three explicit examples. In
particular, it follows from the classification that any closed G2-structure
inducing a metric that is both conformally flat and complete must be equivalent
to the flat G2-structure on $\mathbb{R}^7.$
