A forced relaxation oscillation is studied for a simple circuit consisting of a neon bulb, a resistor, a constant voltage source and a sinusoidal voltage source. Not only the well-known subharmonic mode but a period doubling and chaotic behavior are also observed. The neon bulb is modelled by a series connection of an inductance and a current-controlled nonlinear resistor. In this model, a stray capacitance of the circuit is also introduced, and an inductance, of the neon bulb is assumed only in the discharge phase. A second-order (but the first-order without discharge) nonautonomous ordinary differential equation is obtained, which is shown to explain the general feature of the system with the aid of a one-dimensional return map.