For any closed hyperbolic manifold of dimension $n \geq 3$, suppose asequenceof $n$-cycles representing the fundamental homology class have normsconvergingto the Gromov invariant. We show that this sequence must converge tothe uniform measure on the space ofmaximal-volume ideal simplices. As a corollary, we show that for a hyperbolic$n$-manifold $L$ ($n \geq 3$) with totally-geodesic boundary, the Gromov normof ($L,\partial L$) is strictly greater than the volume of $L$ divided by themaximal volume of an ideal $n$-simplex.