Neutrinoless double beta decay (0νββ) processes sample a wide range of intermediate forbidden nuclear transitions, which may be impacted by quenching of the axial vector coupling constant (g_{A}/g_{V}), the uncertainty of which plays a pivotal role in determining the sensitivity reach of 0νββ experiments. In this Letter, we present measurements performed on a high-resolution LiInSe_{2} bolometer in a "source=detector" configuration to measure the spectral shape of the fourfold forbidden β decay of ^{115}In. The value of g_{A}/g_{V} is determined by comparing the spectral shape of theoretical predictions to the experimental β spectrum taking into account various simulated background components as well as a variety of detector effects. We find evidence of quenching of g_{A}/g_{V} at >5σ with a model-dependent quenching factor of 0.655±0.002 as compared to the free-nucleon value for the interacting shell model. We also measured the ^{115}In half-life to be [5.18±0.06(stat)_{-0.015}^{+0.005}(sys)]×10^{14} yr within the interacting shell model framework. This Letter demonstrates the power of the bolometeric technique to perform precision nuclear physics single-β decay measurements, which along with improved nuclear modeling can help reduce the uncertainties in the calculation of several decay nuclear matrix elements including those used in 0νββ sensitivity calculations.