Chopping between the source and 1 or 2 background positions was an ISOPHOT observing mode for faint source photometry. More than 7000 observations of this type were performed during the mission. We review the main instrumental effects related to chopping, and describe the data reduction steps and calibration strategies developed for this mode. A robust signal processing has been invented which allows to derive reliable difference signals from a chopped pattern. Signal losses dependent on chopper frequency and flux change have been assessed from comparison with staring observations. Chopper offsets have been investigated from the analysis of non-detection measurements. The current data reduction scheme, as implemented in the automatic processing of OLP10, achieves accuracies in general better than 30%. Far-infrared observations of faint sources close to the detection limit may have higher uncertainties, partly due to cirrus confusion which is a severe limitation of this observing mode.