A mirror twin boundary (MTB) in a transition metal dichalcogenide monolayer can host one-dimensional electron liquid of a topological nature with tunable interactions. Unfortunately, electrical characterization of such boundaries has been challenging due to the paucity of samples with large enough size and high quality. Here, we report the conductance measurements of individual MTBs in epitaxially grown monolayer molybdenum disulfide bicrystals that are tens of micrometers long. These MTBs exhibit power-law behaviors of conductance as a function of temperature and bias voltage up to room temperature, consistent with electrons tunneling into a Luttinger liquid. Transport measurements of two distinct types of MTBs reveal the critical role of the atomic-scale defects. This study demonstrates that MTBs in transition metal dichalcogenide monolayers provide an exciting new platform for studying the interplay between electronic interactions and topology.