  We define a new kind of algebroid which fulfills a Leibniz rule, a Jacobi
identity twisted by a 3-form $H$ with values in the kernel of the anchor map,
and the twist is closed under a naturally occurring exterior covariant
derivative. We give examples and define three kinds of cohomology two via
realization as Q-structure on graded manifolds. This classifies PQ3-manifolds.
