We present narrowband images of two externally illuminated circumstellar disks embedded in the Orion Nebula. The images were taken with camera 2 of the Near-Infrared Camera and Multiobject Spectrometer (NICMOS) as part of the Hubble Space Telescope Early Release Observations program. Molecular hydrogen emission is confined to the silhouettes embedded in the objects HST 10 (182-413) and HST 17 (183-419). This emission appears to trace the surfaces of nearly edge-on circumstellar disks and is likely to be excited by the intense far-ultraviolet (FUV) radiation field produced by nearby O stars. The presence of this emission confirms that FUV radiation penetrates to the disk surface. The absence of H2 emission in the region between the ionization front and the disk surface provides evidence that this medium is predominantly atomic. Our observations constitute the first demonstration that the dense circumstellar disks embedded in the proplyds are predominately molecular. While the central star is marginally detected at 2.15 μm in HST 10, the central star of HST 17 is clearly detected.