We report the collective magnetism of the metallic altermagnet CrSb. Magnetic susceptibility and polarized neutron diffraction measurements show that CrSb is a perfectly compensated Ising altermagnet below a Néel temperature of T_N = 733(4) K. Inelastic neutron scattering experiments reveal coherent and highly-dispersive antiferromagnetic spin waves with large group velocities of 61(2) km s⁻¹ and 58(2) km s⁻¹ along the in-plane and out-of-plane directions, respectively. The observed magnon dispersions along high-symmetry directions of the Brillouin zone are well described by a minimal Heisenberg model up to third nearest neighbors of alternating antiferromagnetic and ferromagnetic character, J₁ = 23(4) meV, J₂ = -5.4(8) meV, J₃ = 5.2(8) meV, and an Ising single-ion anisotropy term D = 0.15(4) meV. We observe clear momentum space signatures of chiral spin splitting along the low-symmetry Γ-L direction, characteristic of higher-order altermagnetic exchange interactions, the first such observation in a metallic altermagnet. These findings identify CrSb as a singular material: a metallic altermagnet in which coherent spin-split magnons persist well above room temperature, providing a compelling platform for spintronic applications.