We use angle-resolved photoemission spectroscopy to revisit the electronic structure of BiTeI, previously identified as a polar semiconductor with giant bulk Rashba splitting. We propose an alternative description, which is based on the experimentally determined crystal structure and agrees well with resistivity, quantum oscillations,and optical measurements. BiTeI emerges as a topological 3D Dirac semimetal hosting only two, well isolated from each other and rest of the band structure, Dirac points. Properly doped bulk material or the controlled synthesis of iodine-terminated surface of the pristine material promise to become a canonical condensed matter system whose physical properties are completely defined by the behavior of fourfold fermions.