A search for a very light Higgs boson decaying into a pair of τ leptons is presented within the framework of the next-to-minimal supersymmetric standard model. This search is based on a data set corresponding to an integrated luminosity of 19.7 fb−1 of proton-proton collisions collected by the CMS experiment at a centre-of-mass energy of 8 TeV. The signal is defined by the production of either of the two lightest scalars, h1 or h2, via gluon-gluon fusion and subsequent decay into a pair of the lightest Higgs bosons, a1 or h1. The h1 or h2 boson is identified with the observed state at a mass of 125 GeV. The analysis searches for decays of the a1 (h1) states into pairs of τ leptons and covers a mass range for the a1 (h1) boson of 4 to 8 GeV. The search reveals no significant excess in data above standard model background expectations, and an upper limit is set on the signal production cross section times branching fraction as a function of the a1 (h1) boson mass. The 95% confidence level limit ranges from 4.5 pb at $$ {m}_{{\mathrm{a}}_1} $$ $$ \left({m}_{{\mathrm{h}}_1}\right)=8 $$ GeV to 10.3 pb at $$ {m}_{{\mathrm{a}}_1} $$ $$ \left({m}_{{\mathrm{h}}_1}\right)=5 $$ GeV.