We report the first observation of D+→τ+ντ with a significance of 5.1σ. We measure B(D+→τ+ντ)=(1.20±0.24stat±0.12syst)×10-3. Taking the world average B(D+→μ+νμ)=(3.74±0.17)×10-4, we obtain Rτ/μ=Γ(D+→τ+ντ)/Γ(D+→μ+νμ)=3.21±0.64stat±0.43syst., which is consistent with the standard model expectation of lepton flavor universality. Using external inputs, our results give values for the D+ decay constant fD+ and the Cabibbo-Kobayashi-Maskawa matrix element |Vcd| that are consistent with, but less precise than, other determinations. © 2019 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/" Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.