A Venn diagram for n sets is a collection of n simple closed curves in the plane, {₁, ₂ ... _n}, with the property that for each subset S of the set {1, 2, ..., n} the region is nonempty and connected.

It is known that Venn diagrams for n-sets exist for all n 1 and that Venn diagrams with n-fold rotational symmetry cannot exist unless n is prime. But it has been an open question whether symmetric Venn diagrams exist for all prime n. We show this is always possible by exploiting some interesting properties of of a well-known symmetric chain decomposition in the Boolean lattice.

This is joint work with Charles Killian and Jerrold Griggs.