Elastic electron-proton scattering (e-p) and the spectroscopy of hydrogen atoms are the two methods traditionally used to determine the proton charge radius, r_p . In 2010, a new method using muonic hydrogen atoms¹ found a substantial discrepancy compared with previous results² , which became known as the 'proton radius puzzle'. Despite experimental and theoretical efforts, the puzzle remains unresolved. In fact, there is a discrepancy between the two most recent spectroscopic measurements conducted on ordinary hydrogen^3,4 . Here we report on the proton charge radius experiment at Jefferson Laboratory (PRad), a high-precision e-p experiment that was established after the discrepancy was identified. We used a magnetic-spectrometer-free method along with a windowless hydrogen gas target, which overcame several limitations of previous e-p experiments and enabled measurements at very small forward-scattering angles. Our result, r_p  = 0.831 ± 0.007_stat  ± 0.012_syst  femtometres, is smaller than the most recent high-precision e-p measurement⁵ and 2.7 standard deviations smaller than the average of all e-p experimental results⁶ . The smaller r_p we have now measured supports the value found by two previous muonic hydrogen experiments^1,7 . In addition, our finding agrees with the revised value (announced in 2019) for the Rydberg constant⁸ -one of the most accurately evaluated fundamental constants in physics.