We present optical, near- and mid-infrared imaging of the host galaxy of FRB 121102 with the Gemini North telescope, the Hubble Space Telescope and the Spitzer Space Telescope. The FRB 121102 host galaxy is resolved, revealing a bright star forming region located in the outskirts of the irregular, low-metallicity dwarf galaxy. The star forming region has a half-light radius of 0.68 kpc (0.20 arcsec), encompassing the projected location of the compact (<0.7 pc), persistent radio source that is associated with FRB 121102. The half-light diameter of the dwarf galaxy is 5 to 7 kpc, and broadband spectral energy distribution fitting indicates that it has a total stellar mass of M*~10^8 Msun. The metallicity of the host galaxy is low, 12+log10 ([O/H])=8.0+-0.1. The properties of the host galaxy of FRB 121102 are comparable to those of extreme emission line galaxies, also known to host hydrogen-poor superluminous supernovae and long-duration gamma-ray bursts. The projected location of FRB 121102 within the star forming region supports the proposed connection of FRBs with newly born neutron stars or magnetars.
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