A Hot Jupiter that is tidally locked with its star and that also tidally locks its star's rotation. The length of day of the star, orbit period of the planet, and length of day of the planet are all the same. Tau Bootis b was the first known case of this.
Tau Bootis System - Contains one of the first four discovered Hot Jupiters, which was one of the largest, hottest, closest in (P = 3.3d, a = 0.05) of the earlier discovered ones and the closest known at the time and is today one of the brightest planets known. It was immediately recognized to have tidally locked its star's rotation period. The star (also known as HR 5185) is nearby (50 ly), 1.5 times as massive as the sun. The planet does not transit its star, but is one of the brightest planets known. Several attempts to detect light were declared, but then refuted. In one such attempt by British astronomers, it was nicknamed the "Millenium Planet", and light was thought to have been detected (thought to be a first) by subtracting its star's light, giving an inclination of 29deg, mass of 8 MJ, and size of 1.8 RJ, and blue-green color. NASA's Spitzers later was thought to have detected it (again, a believed first, considering visually detected ones were planetary "candidates"). It was finally detected later by observing CO lines produced by reflected light through its atmosphere, yielding a mass of 6 MJ and inclination of 44F. Water was later also detected in its atmosphere in the near infra-red, the first for any non-transiting exo-planet. The temperature was unexpectedly found to be cooler at the upper levels, unlike many other hot Jupiters (strong ultraviolet radiation are thought to destroy the compounds responsible for creating thermal inversions in this case). The star was the first to have its magnetosphere detected (which envelopes the planet) and also the first known to magnetically flip like the Sun (flips once every Earth year, vs the Sun's 11 years). One of the first 20 exoplanet systems allowed to be given common names by the IAU, but the only one whose chosen name was rejected because it did not conform to IAU's naming standards.