  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.
