At the core of the “proton radius puzzle” is a four–standard deviation discrepancy between the proton root-mean-square charge radii (*r*_{p}) determined from the regular hydrogen (H) and the muonic hydrogen (µp) atoms. Using a cryogenic beam of H atoms, we measured the 2S-4P transition frequency in H, yielding the values of the Rydberg constant *R*_{∞} = 10973731.568076(96) per meterand *r*_{p} = 0.8335(95) femtometer. Our *r*_{p} value is 3.3 combined standard deviations smaller than the previous H world data, but in good agreement with the µp value. We motivate an asymmetric fit function, which eliminates line shifts from quantum interference of neighboring atomic resonances.