Cold atomic hydrogen clouds are the precursors of molecular clouds. Due to self-absorption, the opacity of cold atomic hydrogen may be high, and this gas may constitute an important mass component of the interstellar medium. Atomic hydrogen gas can be cooled to temperatures much lower than found in the cold neutral medium through collisions with molecular hydrogen. In this paper, we search for H i narrow self-absorption (HINSA) features in the Large Magellanic Cloud (LMC) as an indicator of such cold H i clouds, and use the results to quantify atomic masses and atomic-to-molecular gas ratio. Our search for HINSA features was conducted toward molecular clouds in the LMC using the ATCA+Parkes H i survey and the MAGMA CO survey. HINSA features are prevalent in the surveyed sightlines. This is the first detection of HINSA in an external galaxy. The HINSA-HI/H2 ratio in the LMC varies from 0.5 × 10-3 to 3.4 × 10-3 (68% interval), with a mean value of (1.31 ± 0.03) × 10-3, after correcting for the effect of foreground H i gas. This is similar to the Milky Way value and indicates that similar fractions of cold gas exist in the LMC and the Milky Way, despite their differing metallicities, dust content and radiation fields. The low ratio also confirms that, as with the Milky Way, the formation timescale of molecular clouds is short. The ratio shows no radial gradient, unlike the case for stellar metallicity. No correlation is found between our results and those from previous H i absorption studies of the LMC.