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We present the discovery and follow-up observations of SN 2008jb, a core-collapse supernova in the southern dwarf irregular galaxy ESO 302-14 (M_B= -15.3 mag) at 9.6 Mpc. This nearby transient was missed by galaxy-targeted surveys and was only found in archival optical images obtained by the Catalina Real-time Transient Survey and the All-Sky Automated Survey. The well-sampled archival photometry shows that SN 2008jb was detected shortly after explosion and reached a bright optical maximum, V_max≃ 13.6 mag (M_V, max_≃ -16.5). The shape of the light curve shows a plateau of ∼100 days, followed by a drop of ∼1.4 mag in the V band to a slow decline with an approximate ⁵⁶Co decay slope. The late-time light curve is consistent with 0.04±0.01 M_☉ of ⁵⁶Ni synthesized in the explosion. A spectrum of the supernova obtained two years after explosion shows a broad, boxy Hα emission line, which is unusual for normal Type II-Plateau supernovae at late times. We detect the supernova in archival Spitzer and WISE images obtained 8-14 months after explosion, which show clear signs of warm (600-700 K) dust emission. The dwarf irregular host galaxy, ESO 302-14, has a low gas-phase oxygen abundance, 12 + log(O/H) = 8.2 (∼1/5 Z_☉), similar to those of the Small Magellanic Cloud and the hosts of long gamma-ray bursts and luminous core-collapse supernovae. This metallicity is one of the lowest among local ( ≲ 10 Mpc) supernova hosts. We study the host environment using GALEX far-UV, R-band, and Hα images and find that the supernova occurred in a large star formation complex. The morphology of the Hα emission appears as a large shell (R ≃ 350 pc) surrounding the FUV and optical emission. Using the Hα-to-FUV ratio and FUV and R-band luminosities, we estimate an age of ∼9 Myr and a total mass of ∼2x10⁵ M_☉ for the star formation complex, assuming a single-age starburst. These properties are consistent with the expanding Hα supershells observed in many well-studied nearby dwarf galaxies, which are tell-tale signs of feedback from the cumulative effect of massive star winds and supernovae. The age estimated for the star-forming region where SN 2008jb exploded suggests a relatively high-mass progenitor star with an initial mass M ∼ 20 M_☉ and warrants further study. We discuss the implications of these findings in the study of core-collapse supernova progenitors.