Classical novae are expected to contribute to the 1809-keV Galactic \gamma -ray emission by producing its precursor ^ { 26 } Al , but the yield depends on the thermonuclear rate of the unmeasured ^ { 25 } Al ( p, \gamma ) ^ { 26 } Si reaction . Using the \beta decay of ^ { 26 } P to populate the key J ^ { \pi } = 3 ^ { + } resonance in this reaction , we report the first evidence for the observation of its exit channel via a 1741.6 \pm 0.6 ( \textrm { stat } ) \pm 0.3 ( \textrm { syst } ) keV primary \gamma ray , where the uncertainties are statistical and systematic , respectively . By combining the measured \gamma -ray energy and intensity with other experimental data on ^ { 26 } Si , we find the center-of-mass energy and strength of the resonance to be E _ { r } = 414.9 \pm 0.6 ( \textrm { stat } ) \pm 0.3 ( \textrm { syst } ) \pm 0.6 ( \textrm { lit . } ) keV and \omega \gamma = 23 \pm 6 ( \textrm { stat } ) ^ { +11 } _ { -10 } ( \textrm { lit . } ) meV , respectively , where the last uncertainties are from adopted literature data . We use hydrodynamic nova simulations to model ^ { 26 } Al production showing that these measurements effectively eliminate the dominant experimental nuclear-physics uncertainty and we estimate that novae may contribute up to 30 % of the Galactic ^ { 26 } Al . PACS numbers : 23.20.Lv , 25.40.Lw , 26.30.Ca , 27.30.+t