We have measured the absolute frequency of the hydrogen 1S{endash}2S two-photon resonance with an accuracy of 3.4 parts in 10{sup 13} by comparing it with the 28th harmonic of a methane-stabilized 3.39 {mu}m He-Ne laser. A frequency mismatch of 2.1 THz at the 7th harmonic is bridged with a phase-locked chain of five optical frequency interval dividers. From the measured frequency f{sub 1S{endash}2S}=2466061413187.34(84) kHz and published data of other authors we derive precise new values of the Rydberg constant, R{sub {infinity}}=10973731.568639(91) m{sup {minus}1} and of the Lamb shift of the 1S ground state, L{sub 1S}=8172.876(29) MHz. These are now the most accurate values available. {copyright} {ital 1997} {ital The American Physical Society}