We present Atacama Large Millimeter/submillimeter Array observations of 99.02 GHz free-free and H40alpha emission from the centre of the nearby starburst galaxy NGC 253. We calculate electron temperatures of 3700-4500 K for the photoionized gas, which agrees with previous measurements, and we measure a star formation rate of 1.73+/-0.12 M_solar/yr within the central 20x10 arcsec, which fall within the broad range of measurements from previous millimetre and radio observations but which are better constrained. We also demonstrate that the dust opacities are ~3 dex higher than inferred from previous near-infrared data, which illustrates the benefits of using millimetre star formation tracers in very dusty sources.