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, h${1}$ or h${2}$, via gluon-gluon fusion and subsequent decay into a pair of the lightest Higgs bosons, a${1}$ or h${1}$. The h${1}$ or h${2}$ boson is identified with the observed state at a mass of 125 GeV. The analysis searches for decays of the a${1}$ (h${1}$) states into pairs of τ leptons and covers a mass range for the a${1}$ (h${1}$) 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 a${1}$ (h${1}$) 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.