Topological semimetals are materials whose band structure contains touching points that are topologically nontrivial and can host quasiparticle excitations that behave as Dirac or Weyl fermions^,,,,,,. These so-called Weyl points not only exist in electronic systems, but can also be found in artificial periodic structures with classical waves, such as electromagnetic waves in photonic crystals^,,, and acoustic waves in phononic crystals^,. Due to the lack of spin and a difficulty in breaking time-reversal symmetry for sound, however, topological acoustic materials cannot be achieved in the same way as electronic or optical systems. And despite many theoretical predictions^,, experimentally realizing Weyl points in phononic crystals remains challenging. Here, we experimentally realize Weyl points in a chiral phononic crystal system, and demonstrate surface states associated with the Weyl points that are topological in nature, and can host modes that propagate only in one direction. As with their photonic counterparts, chiral phononic crystals bring topological physics to the macroscopic scale.