We present aperture synthesis imaging of dense molecular gas in the Large Magellanic Cloud, taken with the prototype millimeter receivers of the Australia Telescope Compact Array (ATCA). Our observations of the N113 H II region reveal a condensation with a size of ~6'' (1.5 pc) FWHM, detected strongly in the 1-0 lines of HCO+, HCN, and HNC, and weakly in C2H. Comparison of the ATCA observations with single-dish maps from the Mopra Telescope and sensitive spectra from the Swedish-ESO Submillimetre Telescope indicates that the condensation is a massive clump of ~104 M☉ within a larger ~105 M☉ molecular cloud. The clump is centered adjacent to a compact, obscured H II region that is part of a linear structure of radio continuum sources extending across the molecular cloud. We suggest that the clump represents a possible site for triggered star formation. Examining the integrated line intensities as a function of interferometer baseline length, we find evidence for decreasing HCO+/HCN and HCN/HNC ratios on longer baselines. These trends are consistent with a significant component of the HCO+ emission arising in an extended clump envelope and a lower HCN/HNC abundance ratio in dense cores.