Recently, LHAASO has discovered more than 40 ultra-high-energy gamma-ray sources, opening a new window in ultra-high-energy gamma-ray astronomy. Notably, most of these sources exhibit extended characteristics that require telescopes with higher angular resolution and sensitivity to observe and study their morphology. Thus, we propose a new project: the Large Array of Imaging Atmospheric Cherenkov Telescopes (LACT). LACT is designed to consist of 32 telescopes, each achieving an angular resolution better than 0.05° above 10 TeV. These telescopes will be constructed within the LHAASO detector array, utilizing LHAASO unique muon detector array to provide superior gamma-proton discrimination at ultra-high energies. This will significantly enhance the detection sensitivity of gamma rays above 10 TeV, offering an unparalleled advantage over other IACT experiments globally. For gamma rays above 100TeV, the sensitivity of 500 hours of exposure on a single source is designed to match the sensitivity of one year of exposure to LHAASO. This capability will enable us to identify gamma-ray sources in PeVatrons and measure their morphology in detail, aiding in the understanding of gamma-ray emission mechanisms and the exploration of the origins of high-energy cosmic rays. Each LACT telescope has a field of view of 8° with a pixel size of 0.2°. This paper introduces the design concept, performance parameters, prototype development progress, and future construction plans for LACT.