  Black holes have been found over a wide range of masses, from stellar
remnants with masses of 5-150 solar masses (Msun), to those found at the
centers of galaxies with $M>10^5$ Msun. However, only a few debated candidate
black holes exist between 150 and $10^5$ Msun. Determining the population of
these intermediate-mass black holes is an important step towards understanding
supermassive black hole formation in the early universe. Several studies have
claimed the detection of a central black hole in $\omega$ Centauri, the Milky
Way's most massive globular cluster. However, these studies have been
questioned due to the possible mass contribution of stellar mass black holes,
their sensitivity to the cluster center, and the lack of fast-moving stars
above the escape velocity. Here we report observations of seven fast-moving
stars in the central 3 arcseconds (0.08 pc) of $\omega$ Centauri. The
velocities of the fast-moving stars are significantly higher than the expected
central escape velocity of the star cluster, so their presence can only be
explained by being bound to a massive black hole. From the velocities alone, we
can infer a firm lower limit of the black hole mass of $\sim$8,200 Msun, making
this a compelling candidate for an intermediate-mass black hole in the local
universe.
