The MuCap experiment at the Paul Scherrer Institute has measured the rate Λ(S) of muon capture from the singlet state of the muonic hydrogen atom to a precision of 1%. A muon beam was stopped in a time projection chamber filled with 10-bar, ultrapure hydrogen gas. Cylindrical wire chambers and a segmented scintillator barrel detected electrons from muon decay. Λ(S) is determined from the difference between the μ(-) disappearance rate in hydrogen and the free muon decay rate. The result is based on the analysis of 1.2 × 10(10) μ(-) decays, from which we extract the capture rate Λ(S) = (714.9 ± 5.4(stat) ± 5.1(syst)) s(-1) and derive the proton's pseudoscalar coupling g(P)(q(0)(2) = -0.88 m(μ)(2)) = 8.06 ± 0.55.