Here we report on the first CENAM realization of the phase-shift method for chromatic dispersion measurements in mono-mode dispersion-shifted optical fibers used for the telecommunications C-band (1 530 nm to 1 565 nm). This chromatic dispersion measurement and calibration capability development at CENAM will provide the Mexican telecommunications industry with a formally established SI unit's traceability source, thus enhancing this rapidly growing and high impact economic sector competitiveness in Mexico. We also identified a 40 MHz modulation frequency, a 2.5 nm wavelength step and the 1 535 nm to 1 570 nm wavelength scanning range, as the optimum experimental parameters that have to be set in order to obtain experimental data which numerical Sellmeier polynomials fittings produce representative determinations for the group delay and the chromatic dispersion. We also obtained 1 549.388 nm ± 0.098 nm, for coverage factor k=1, for the zero dispersion wavelength, and 0.719 7 ps·nm -2 ± 0.005 5 ps·nm -2 , (k=1), for the zero dispersion slope of the tested optical fiber.