We seek evidence for secondary star formation in the Large Magellanic Cloud (LMC) arising in gas compressed by the interactions between H I supergiant shells (SGS) identified from the Australia Telescope Compact Array (ATCA) survey of Kim et al., using mid-infrared (MIR) images from the Midcourse Space Experiment (MSX), and radio continuum images from the Molonglo Observatory Synthesis Telescope (MOST). We identify a dense photodissociation region shaped like a bar that lies between the rims of LMC 4 and LMC 5 as a strong candidate for this process, and argue that it has produced the young associations LH 52 and 53 in the dense starfield of NGC 1948 within the past few Myr. No obvious stellar candidate matches the coincident 8.3-, 21.3-mum, and 843-MHz peaks in this bar, although this bright spot lies between two nebulous Halpha patches. At least one other such H I-MIR bar exists in the LMC so that this mode of star formation is unlikely to have been a unique occurrence. We have found a correlation between 8.3-mum radiance and H I column density for the LMC in general that can be predicted from the Schmidt law for spiral galaxies.