During the July 2002 CRYSTAL-FACE field program based from Key West, Florida, aircraft measurements showed that long-lived thin tropopause cirrus (TTC) layers were often present above thunderstorm anvils. This paper describes these clouds and explores their possible origins. Measurements showed that the horizontal dimensions of TTC layers were nearly identical to convectively formed anvils beneath, but that TTC did not appear to have originated from convective detrainment. Rather, they appeared to have formed in stably stratified air derived from high altitudes near the tropopause. TTC were separated vertically from the top of the anvil by ~1 km, they lacked precipitation particles, and they were strongly depleted in HDO, all of which indicate in situ formation. However, compared to surrounding clear air near the tropopause, TTC were enriched in moisture and trace gases. The degree of enrichment was consistent with mixing of air near the tropopause with the same convective air mass that produced the anvil. Unlike surrounding air, TTC had embedded a monochromatic gravity wave with a wavelength of 2 km and an amplitude of several hundred meters. This evidence, supported by a photograph from CRYSTAL-FACE, leads to the conjecture that TTC originate as stratiform pileus clouds that form near the tropopause ahead of vigorous convective uplift. We hypothesize that the pileus are penetrated by the convection, moistened through turbulent mixing, and once the convection subsides, they are sustained by radiative cooling due to the presence of the anvil layer beneath.