A quasiperiodic route to chaos is investigated experimentally and theoretically in a current‐carrying unstable ion sheath. A quasiperiodic regime with two frequencies is realized by a coherent instability and an external periodic oscillation. Chaos appears directly from the quasiperiodic regime when the amplitude of the external oscillation is increased, making nonlinear effects more important. A correlation dimension and the largest Lyapunov exponent, obtained experimentally in the chaotic regime, confirm that the observed chaos is deterministic and the attractor is strange. A period‐doubling route to chaos is also observed after the instability is quenched with the external oscillation by increasing the amplitude of the external oscillation further. These experimental results are in fair agreement with a theory that describes ion dynamics in the ion sheath.