We report the first observation of D^{+}→τ^{+}ν_{τ} with a significance of 5.1σ. We measure B(D^{+}→τ^{+}ν_{τ})=(1.20±0.24_{stat}±0.12_{syst})×10^{-3}. Taking the world average B(D^{+}→μ^{+}ν_{μ})=(3.74±0.17)×10^{-4}, we obtain R_{τ/μ}=Γ(D^{+}→τ^{+}ν_{τ})/Γ(D^{+}→μ^{+}ν_{μ})=3.21±0.64_{stat}±0.43_{syst}., which is consistent with the standard model expectation of lepton flavor universality. Using external inputs, our results give values for the D^{+} decay constant f_{D^{+}} and the Cabibbo-Kobayashi-Maskawa matrix element |V_{cd}| that are consistent with, but less precise than, other determinations.