ABSTRACT We present new measurements of the flux power-spectrum P(k) of the z < 0.5 H i Lyman-α Forest spanning scales $k \sim 0.001\!-\!0.1\, \mathrm{s \, km}^{-1}$. These results were derived from 65 far-ultraviolet quasar spectra (resolution $R \sim 18\, 000$) observed with the Cosmic Origin Spectrograph (COS) on board the Hubble Space Telescope. The analysis required careful masking of all contaminating, coincident absorption from H i and metal–line transitions of the Galactic interstellar medium and intervening absorbers as well as proper treatment of the complex COS line-spread function. From the P(k) measurements, we estimate the H i photoionization rate ($\Gamma _{\rm H\,{\small I}}$) in the z < 0.5 intergalactic medium. Our results confirm most of the previous $\Gamma _{\rm H\,{\small I}}$ estimates. We conclude that previous concerns of a photon underproduction crisis are now resolved by demonstrating that the measured $\Gamma _{\rm H\,{\small I}}$ can be accounted for by ultraviolet emission from quasars alone. In a companion paper, we will present constraints on the thermal state of the z < 0.5 intergalactic medium from the P(k) measurements presented here.