We present the discovery and follow-up observations of SN 2008jb, a core-collapse supernova in the dwarf irregular galaxy ESO 302-14 at 9.6 Mpc. This transient was missed by galaxy-targeted surveys and was only found in archival optical images obtained by CRTS and ASAS. It was detected shortly after explosion and reached a bright optical maximum, Vmax = 13.6 mag (M_Vmax ~ -16.5). The shape of the light curve shows a plateau of 100 days, followed by a drop of 1.4 mag in V-band to a decline with the approximate Co 56 decay slope, consistent with 0.04 Msun of Ni 56 synthesized in the explosion. A spectrum obtained 2 years after explosion shows a broad, boxy Halpha emission line, which is unusual for type IIP supernovae. We detect the supernova in archival Spitzer and WISE images obtained 8-14 months after explosion, which show clear signs of warm dust emission. The dwarf irregular host galaxy has a low gas-phase oxygen abundance, 12 + log(O/H) = 8.2 (~1/5 Solar), similar to those of the SMC and the hosts of long gamma-ray bursts and luminous core-collapse supernovae. We study the host environment using GALEX FUV, R-band, and Halpha images and find that the supernova occurred in a large star-formation complex. The morphology of the Halpha emission appears as a large shell (R = 350 pc) surrounding the FUV and optical emission. We estimate an age of ~9 Myr and a total mass of ~2 x 10^5 Msun for the star-formation complex. These properties are consistent with the expanding Halpha supershells observed in 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 suggests a relatively high-mass progenitor star with initial mass of ~20 Msun. We discuss the implications of these findings in the study of core-collapse supernova progenitors. (Abridged)