In recent years, there has been a great deal of progress on ideas related to twisted supergravity, building on the definition given by Costello and Li. Much of what is explicitly known about these theories comes from the topological B-model, whose string field theory conjecturally produces the holomorphic twist of type IIB supergravity. Progress on eleven-dimensional supergravity has been hindered, in part, by the lack of such a worldsheet approach. I will discuss a rigorous computation of the twist of the free eleven-dimensional supergravity multiplet, as well as an interacting BV theory with this field content that passes a large number of consistency checks. Surprisingly, the resulting holomorphic theory on flat space is closely related to the infinite-dimensional exceptional simple Lie superalgebra E(5|10), and another such exceptional simple algebra—E(3|6)—appears in the context of M5-branes. This is joint work with Surya Raghavendran and Brian Williams.