  We present a systematic study of both the temperature and frequency
dependence of the optical response in TaAs, a material that has recently been
realized to host the Weyl semimetal state. Our study reveals that the optical
conductivity of TaAs features a narrow Drude response alongside a conspicuous
linear dependence on frequency. The width of the Drude peak decreases upon
cooling, following a $T^{2}$ temperature dependence which is expected for Weyl
semimetals. Two linear components with distinct slopes dominate the 5-K optical
conductivity. A comparison between our experimental results and theoretical
calculations suggests that the linear conductivity below $\sim$230~cm$^{-1}$ is
a clear signature of the Weyl points lying in very close proximity to the Fermi
energy.
