The ESO spectrograph famous for high-precision radial-velocity exoplanet discoveries is HARPS.
HARPS stands for High Accuracy Radial Velocity Planet Searcher. It is a stabilized, high-resolution echelle spectrograph designed to detect the tiny Doppler shifts caused when an orbiting planet makes its host star move toward and away from Earth. The method measures the star’s radial velocity rather than seeing the planet directly.
HARPS was installed on ESO’s 3.6-metre telescope at La Silla Observatory in Chile. It achieved first light in 2003 and became one of the leading precision instruments in exoplanet science, particularly for finding small planets around nearby stars. Its design uses extreme thermal and mechanical stability and a simultaneous reference spectrum to keep measurements consistent.
The other options are different ESO instruments or facilities. ALMA is a radio observatory, SPHERE is optimized for high-contrast imaging, and MUSE is an optical integral-field spectrograph. HARPS has also had a southern counterpart, HARPS-N, at the Telescopio Nazionale Galileo in the Canary Islands.