The Tarantula Nebula in the Large Magellanic Cloud is known for its high star formation activity. At its center lies the young massive star cluster R136, providing a significant amount of the energy that makes the nebula shine so brightly at many wavelengths. Recently, young massive star clusters have been suggested to also efficiently produce high-energy cosmic rays, potentially beyond PeV energies. Here, we report the detection of very-high-energy $\gamma$-ray emission from the direction of R136 with the High Energy Stereoscopic System, achieved through a multicomponent, likelihood-based modeling of the data. This supports the hypothesis that R136 is indeed a very powerful cosmic-ray accelerator. Moreover, from the same analysis, we provide an updated measurement of the $\gamma$-ray emission from 30 Dor C, the only superbubble detected at TeV energies presently. The $\gamma$-ray luminosity above $0.5\,\mathrm{TeV}$ of both sources is $(2-3)\times 10^{35}\,\mathrm{erg}\,\mathrm{s}^{-1}$. This exceeds by more than a factor of 2 the luminosity of HESS J1646$-$458, which is associated with the most massive young star cluster in the Milky Way, Westerlund 1. Furthermore, the $\gamma$-ray emission from each source is extended with a significance of $>3\sigma$ and a Gaussian width of about $30\,\mathrm{pc}$. For 30 Dor C, a connection between the $\gamma$-ray emission and the nonthermal X-ray emission appears likely. Different interpretations of the $\gamma$-ray signal from R136 are discussed.
