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