The noise level of various monolithic zero-drift amplifiers was measured. Excess current noise was observed that significantly exceeds shot noise calculated from the input bias current. The parameter dependence of the excess noise was studied with a basic chopper realized with discrete components. A linear dependence of the current noise density on the chopper's load capacitance was found. Guided by this observation, a simple model was applied that is based on thermal noise in the input switches. The model predicts a linear scaling of the current noise density with temperature, capacitance, and switching frequency. The experimental verification was performed with the basic chopper operated at room temperature and liquid nitrogen (77 K). Good agreement between theory and experiment was found.