This work explores, from a theoretical viewpoint, the aluminum incorporation into silicate chains with dreierketten conformation relevant in the cementitious calcium-silicate-hydrate (C-S-H) gel and in other minerals, such as wollastonite and hillebrandite. To this end, we have investigated by means of ab initio calculations both the stability and the formation of aluminosilicate chains. Our results show that only certain aluminosilicate chains are stable, namely, those whose tetrahedra length m obey the m = 3n - 1 rule with n = 1, 2, 3,..., in agreement with experiments. Moreover, our detailed analyses explain why Al ions prefer the bridging sites and introduce new insights on the growth process.