The partners in the Magellan Telescopes have formed a core group to collaborate in a project whose goal is the design and construction of one or more 20-meter class telescopes. The conceptual design for the unit telescope is being developed and the status of the work is described here. The design is based on a segmented primary mirror consisting of six off-axis 8.4-meter mirrors arranged in a hexagon. Various concepts with additional mirrors filling in the center have been investigated. An adaptive Gregorian secondary mirror combines the beams in the telescope. The mirrors will be mounted in a single fully-steerable alt-az mount. Survey and testing of prospective sites is underway in Chile.