Fusion neutrons streaming from a burning inertial confinement fusion capsule generate gamma rays via inelastic nuclear scattering in the ablator of the capsule. The intensity of gamma-ray emission is proportional to the product of the ablator areal density (ρR) and the yield of fusion neutrons, so by detecting the gamma rays we can infer the ablator areal density, provided we also have a measurement of the capsule's total neutron yield. In plastic-shell capsules, for example, (12)C nuclei emit gamma rays at 4.44 MeV after excitation by 14.1 MeV neutrons from D+T fusion. These gamma rays can be measured by a new gamma-ray detector under development. Analysis of predicted signals is in progress, with results to date indicating that the method promises to be useful for diagnosing imploded capsules.