We study the direct production of the J^{PC}=1^{++} charmonium state χ_{c1}(1P) in electron-positron annihilation by carrying out an energy scan around the mass of the χ_{c1}(1P). The data were collected with the BESIII detector at the BEPCII collider. An interference pattern between the signal process e^{+}e^{-}→χ_{c1}(1P)→γJ/ψ→γμ^{+}μ^{-} and the background processes e^{+}e^{-}→γ_{ISR}J/ψ→γ_{ISR}μ^{+}μ^{-} and e^{+}e^{-}→γ_{ISR}μ^{+}μ^{-} is observed by combining all the data samples. The χ_{c1}(1P) signal is observed with a significance of 5.1σ. This is the first observation of a C-even state directly produced in e^{+}e^{-} annihilation. The electronic width of the χ_{c1}(1P) resonance is determined to be Γ_{ee}=(0.12_{-0.08}^{+0.13}) eV, which is of the same order of magnitude as theoretical calculations.