The K1V late-type dwarf α Cen B has been monitored to search for spectroscopic variability in the Ca II H chromospheric line during its rotational period. The observations were made with the Coudé Echelle Spectrograph with the 1.4 Coudé Auxiliary Telescope at ESO, with spectral resolution 80000. Variability in flux up to 29 % and profile asymmetries are explained as modulation caused by discrete structures such as solar-like plages on the star surface. An analysis of the visibility and velocity of these structures gives a rotational period of 43 days, in agreement with the Rossby number derived from the Ca II chromospheric flux. A multi-component model is used to estimate the positions and filling factors of such emissive structures. A coherence time up to 6 months is found for the plage signature, but gradual phase shifts and overall flux variations are observed from year to year, providing an information on the emergence/disappearance of active regions and on cyclic effects operating on global activity.