Let Mbar_g be the moduli space of stable curves of genus g. The Euler class of the Hodge bundle is a very important class in the Chow ring of Mbar_g. One of its key properties is that it vanishes on one of the boundary divisors of Mbar_g. I will describe a new class with an analogous boundary vanishing property, as well as a conjectural relationship to the moduli space of bridgeless stable curves. Speaker(s): Aaron Pixton (University of Michigan)