Dirac and Weyl nodal materials can host low-energy relativistic quasiparticles. Under strong magnetic fields, the topological properties of Dirac/Weyl materials can directly be observed through quantum Hall states. However, most Dirac/Weyl nodes generically exist in semimetals without exploitable band gaps due to their accidental band-crossing origin. Here, we report the first experimental observation of Weyl fermions in a semiconductor. Tellurene, the two-dimensional form of tellurium, possesses a chiral crystal structure which induces unconventional Weyl nodes with a hedgehog-like radial spin texture near the conduction band edge. We synthesize high-quality n-type tellurene by a hydrothermal method with subsequent dielectric doping and detect a topologically non-trivial pi Berry phase in quantum Hall sequences. Our work expands the spectrum of Weyl matter into semiconductors and offers a new platform to design novel quantum devices by marrying the advantages of topological materials to versatile semiconductors. The accidental band-crossing origin of Weyl nodes paired with the absence of sizeable band gaps hampers the exploitation of low-energy relativistic quasiparticles in Weyl semimetals. In a gate-tunable high-quality tellurene film, quantum Hall measurements unveil a topologically non-trivial pi Berry phase caused by unconventional Weyl nodes in these tellurium two-dimensional sheets.