Using a tunable diode-laser spectrometer, we have measured N-broadening coefficients of 87 individual rovibrational lines in the P and R branches of the v band of methyl chloride (CHCl) at 203.2 K. These lines with J values ranging from 2 to 22 and K from 0 to 6 are located in the range 711-751 cm. Most of the collisional widths are obtained by modeling the spectral region from the superposition of overlapping Voigt or Rautian profiles. We have reviewed and completed previous measurements of N-broadening coefficients at room temperature in the v band, in order to compare them to the low-temperature data. A semiclassical calculation, including electrostatic, induction, and dispersion energy contributions, has provided results that are in reasonable agreement with the experimental data at room temperature, but generally larger than the data at low temperature for small or medium J values. The temperature dependence of the collisional broadenings derived from a simple power law has been determined both experimentally and theoretically.