Contrary to previous studies that identified the ground state crystal structure of the entire R_3Co series (R is a rare earth) as orthorhombic Pnma, we show that Y_3Co undergoes a structural phase transition at T_t=160K. Single crystal neutron diffraction data reveal that at T_t the trigonal prisms formed by a cobalt atom and its six nearest-neighbor yttrium atoms experience distortions accompanied by notable changes of the Y-Co distances. The formation of the low-temperature phase is accompanied by a pronounced lattice distortion and anomalies seen in heat capacity and resistivity measurements. Density functional theory calculations reveal a dynamical instability of the Pnma structure of Y_3Co. In particular, a transversal acoustic phonon mode along the (00z) direction has imaginary frequencies at z<1/4. Employing inelastic neutron scattering measurements we find a strong damping of the (00z) phonon mode below a critical temperature T_t. The observed structural transformation causes the reduction of dimensionality of electronic bands and decreases the electronic density of states at the Fermi level that identifies Y_3Co as a system with the charge density wave instability.