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We present the first fully calibrated H$_2$, 1-0 S(1) image of the entire 30Doradus nebula. The observations were conducted using the NOAO ExtremelyWide-Field Infrared Imager on the CTIO 4-meter Blanco Telescope. Together witha NEWFIRM Br$\gamma$ image of 30 Doradus, our data reveal the morphologies ofthe warm molecular gas and ionized gas in 30 Doradus. The brightestH$_2$-emitting area, which extends from the northeast to the southwest of R136,is a photodissociation region viewed face-on, while many clumps and pillarfeatures located at the outer shells of 30 Doradus are photodissociationregions viewed edge-on. Based on the morphologies of H$_2$, Br$\gamma$,$^{12}$CO, and 8$\mu$m emission, the H$_2$ to Br$\gamma$ line ratio and Cloudymodels, we find that the H$_2$ emission is formed inside the photodissociationregions of 30 Doradus, 2 - 3 pc to the ionization front of the HII region, in arelatively low-density environment $<$ 10$^4$ cm$^{-3}$. Comparisons withBr$\gamma$, 8$\mu$m, and CO emission indicate that H$_2$ emission is due tofluorescence, and provide no evidence for shock excited emission of this line.

Molecular and Ionized Hydrogen in 30 Doradus. I. Imaging Observations