Let A_g be the moduli space of principally polarized abelian varieties of dimension g. The Hodge bundle is a rank g vector bundle on A_g given by pulling back the relative cotangent bundle of the universal family along the zero section. The top Chern class of the Hodge bundle on A_g vanishes. However, when the Hodge bundle is extended to a compactification of A_g, this top Chern class stops vanishing. I will present a conjectural formula for this top Chern class on the second Voronoi compactification of A_g. The formula is expressed as a piecewise polynomial on the dual cone complex, the moduli space of tropical principally polarized abelian varieties.