The Majorana fermion, which is its own antiparticle and obeys non-Abelian statistics, plays a critical role in topological quantum computing. It can be realized as a bound state at zero energy, called a Majorana zero mode (MZM), in the vortex core of a topological superconductor, or at the ends of a nanowire when both superconductivity and strong spin orbital coupling are present. A MZM can be detected as a zero-bias conductance peak (ZBCP) in tunneling spectroscopy. However, in practice, clean and robust MZMs have not been realized in the vortices of a superconductor because of contamination from impurity states or other closely packed Caroli–de Gennes-Matricon (CdGM) states, which hampers further manipulations of MZMs. Here, using scanning tunneling spectroscopy, we show that a ZBCP well separated from the other discrete CdGM states exists ubiquitously in the cores of free vortices in the defect-free regions of(Li0.84Fe0.16)OHFeSe, which has a superconducting transition temperature of 42 K. Moreover, a Dirac-cone-type surface state is observed by angle-resolved photoemission spectroscopy, and its topological nature is confirmed by band calculations. The observed ZBCP can naturally be attributed to a MZM arising from the chiral topological surface state of a bulk superconductor. Thus,(Li0.84Fe0.16)OHFeSeprovides an ideal platform for studying MZMs and topological quantum computing.