The selection of chiralities of single-walled carbon nanotubes is one of the key problems of nanotube science. We suggest that the chirality-selective growth of SWNTs could be achieved using chemical vapour deposition (CVD) by controlling the type of caps that form during the nucleation stage. As the catalyst can be solid during CVD, the formation of particular caps may be favoured by an epitaxial relationship to the catalyst surface. The corresponding tubes would then grow preferentially. We show by ab-initio calculations that the formation energy of some lattice-matched caps and tubes are 1-2 eV lower than the non lattice-matched structures.