The specific rotation of NaBrO3 single crystals has been measured with an X-ray beam extracted from the white synchrotron radiation spectrum by a specially designed silicon monochromator–polarizer. A detailed description of the monochromator principle and expected performance is given and the characteristics of the output beam are as follows: extremely narrow angular and wavelength spread (Δθ = 7 μrad, Δλ = 8 × 10–6 Å), nearly pure linear polarization (polarization ratio 2.5 × 108). The wavelength has been chosen very close to the bromine K edge (λ − λK = 2 × 10–3 Å) in order to take advantage of possible resonant effects. The experimental set-up is of the crossed-polarizer type, the analyzer being a GaAs crystal adjusted for the 555 reflection with a Bragg angle θA equal to 44.95°. The specific rotation measured in these conditions has been found to be 0.35 ± 0.31° cm−1. An explanation is proposed for this small value.