this talk is based on joint work with murray schacher and eric rains. given three cohomology classes satisfying a certain vanishing condition on cup products, massey defines a triple product [a,b,c] and uses it to prove a jacobi identity in algebraic topology. by construction, the massey product is a coset of a (known) subgroup of cohomology in degree (deg a) + (deg b) + (deg c) - 1. one interesting case is when a,b,c are degree one and the cohomology is the galois cohomology of a field f with gf(2) coefficients. in this context, we can view the massey product of three quadratic extensions of f as a (set of) quaternion division algebras over f. we give an interpretation of [a,b,c] as an obstruction to a lifting problem in galois theory. we give a new formula for [a,b,c], and use it to show that the massey product contains the neutral element.