An increasing sample of Gamma-Ray Bursts (GRBs) observed by Swift show evidence of ‘chromatic breaks’, i.e. breaks that are present in the X-ray but not in the optical. We find that in a significant fraction of these GRB afterglows the X-ray and the optical emission cannot be produced by the same component. We propose that these afterglow lightcurves are the result of a two-component jet, in which both components undergo energy injection for the whole observation and the X-ray break is due to a jet break in the narrow outflow. Bursts with chromatic breaks also explain another surprising finding, the paucity of late achromatic breaks. We propose a model that may explain the behaviour of GRB emission in both X-ray and optical bands. This model can be a radical and noteworthy alternative to the current interpretation for the ‘canonical’ XRT and UVOT lightcurves, and it bears fundamental implications for GRB physics.