We present Hubble Space Telescope NICMOS imaging of the H2 2.12 μm emission in five fields in the Helix Nebula ranging in radial distance from 250'' to 450'' from the central star. The images reveal arcuate structures with their apexes pointing toward the central star. These molecular hydrogen knots are most highly structured in the fields closest to the central star and become increasingly less structured with increasing radius. Comparison of these images with ground-based images of comparable resolution reveals that the molecular gas is more highly clumped than the ionized gas line tracers. From our images, we determine an average number density of knots in the molecular gas ranging from 162 knots arcmin-2 in the denser regions to 18 knots arcmin-2 in the lower density outer regions. The decreasing number density of H2 knots in the outer regions creates a lower filling factor of neutral and molecular gas emission in the radio observations of CO and H I and may explain why these outer regions, where we clearly detect H2 2.12 μm, fall below the detection limit of the radio observations. Using this new number density, we estimate the total number of knots in the Helix to be ~23,000, which is a factor of 6.5 larger than previous estimates. The total neutral gas mass in the Helix is 0.35 M assuming a mass of ~1.5 × 10-5 M for the individual knots. The H2 emission structure of the entire Helix Nebula supports the recent interpretation of the Helix as a nearly pole-on polypolar planetary nebula (PN). The H2 intensity, (5–9) × 10-5 ergs s-1 cm-2 sr-1, remains relatively constant with projected distance from the central star, suggesting a heating mechanism for the molecular gas that is distributed almost uniformly in the knots throughout the nebula. The temperature and H2 2.12 μm intensity of the knots can be approximately explained by photodissociation regions (PDRs) in the individual knots; however, theoretical PDR models of PNs underpredict the intensities of some knots by a factor of 10. The brightest H2 emission (~3 × 10-4 ergs s-1 cm-2 sr-1) may be enhanced by a larger than unity area filling factor of H2 knots or may be an individual H2 knot exposed to direct starlight, causing rapid photoevaporation compared with the more embedded knots of the disk.