We report the identification of very massive stars (VMS; mass > 100 M⊙) that may be segregated in the center of the young massive star cluster at z = 2.37 hosted in the lensed galaxy called Sunburst galaxy. This result is based on two pieces of evidence: (1) VLT/MUSE spectra of several multiple images of the same star cluster show key spectral signatures of VMS, such as the He IIλ1640 broad emission, N IVλ1486 emission, and an N IVλ1720 P Cygni profile. In particular, He IIλ1640 is broad (∼1610 ± 300 km s−1), with an equivalent width of 3 Å, and asymmetric profile. These features require an extremely young (∼2.5 Myr) stellar population component in which the masses of the stars exceed 100 M⊙. When a Salpeter initial mass function and BPASS models for normal massive stars are assumed, the observed spectral features require ∼400 VMS. (2) The same star cluster is detected at a signal-to-noise ratio of ∼100 in the Lyman continuum domain (λ < 900 Å). The Lyman continuum emission emerges from a region with a radius that is at least twice smaller than what is observed at 1700 Å (independently of magnification) and is located in the center of the cluster. After delensing, the effective radii in absolute scales are Reff[LyC] ∼ 4.7 ± 1.5 pc and Reff[1700] = 7.8 ± 1.4 pc. The Lyman continuum radiation is mainly produced by hot and massive stars, which implies that their spatial distribution (including that of VMS) is preferentially more confined in the central parts of the cluster. Approximately 400 VMS hosted by a cluster of ∼107 M⊙ produce ∼15% of the escaping Lyman continuum photons, and the remaining photons are produced by other massive early-type stars.