Using gravitational microlensing, we detected a cold terrestrial planet orbiting one member of a binary star system. The planet has low mass (twice Earth's) and lies projected at similar to 0.8 astronomical units (AU) from its host star, about the distance between Earth and the Sun. However, the planet's temperature is much lower, <60 Kelvin, because the host star is only 0.10 to 0.15 solar masses and therefore more than 400 times less luminous than the Sun. The host itself orbits a slightly more massive companion with projected separation of 10 to 15 AU. This detection is consistent with such systems being very common. Straightforward modification of current microlensing search strategies could increase sensitivity to planets in binary systems. With more detections, such binary-star planetary systems could constrain models of planet formation and evolution.