The 3He(α,γα,γ)7Be and 3H(α,γα,γ)7Li astrophysical S factors are calculated within the no-core shell model with continuum using a renormalized chiral nucleon–nucleon interaction. The 3He(α,γα,γ)7Be astrophysical S factors agree reasonably well with the experimental data while the 3H(α,γα,γ)7Li ones are overestimated. The seven-nucleon bound and resonance states and the α + 3He/3H elastic scattering are also studied and compared with experiment. The low-lying resonance properties are rather well reproduced by our approach. At low energies, the s-wave phase shift, which is non-resonant, is overestimated.