Star-like objects with effective temperatures of less than 2,700 kelvin are referred to as 'ultracool dwarfs'(1). This heterogeneous group includes stars of extremely low mass as well as brown dwarfs (substellar objects not massive enough to sustain hydrogen fusion), and represents about 15 per cent of the population of astronomical objects near the Sun(2). Core-accretion theory predicts that, given the small masses of these ultracool dwarfs, and the small sizes of their protoplanetary disks(3,4), there should be a large but hitherto undetected population of terrestrial planets orbiting them(5)-ranging from metal-rich Mercury-sized planets(6) to more hospitable volatile-rich Earth-sized planets(7). Here we report observations of three short-period Earth-sized planets transiting an ultracool dwarf star only 12 parsecs away. The inner two planets receive four times and two times the irradiation of Earth, respectively, placing them close to the inner edge of the habitable zone of the star(8). Our data suggest that 11 orbits remain possible for the third planet, the most likely resulting in irradiation significantly less than that received by Earth. The infrared brightness of the host star, combined with its Jupiter-like size, offers the possibility of thoroughly characterizing the components of this nearby planetary system.