Transition probabilities for twenty nine lines in Fe I ( 2656≦ λ ≦ 5379 A ̊ ) have been measured by combining beam-foil lifetime measurements for six levels in Fe I with measurements of the branching ratio for all known transitions which depopulate these levels. The lifetime measurements are restricted to highly excited levels ( E > 6 eV) which do not exhibit cascading repopulation. The branching-ratio measurements make use of two monochromators to measure simultaneously (1) the intensity of each line that originates from the level under investigation, and (2) the intensity of a reference line to monitor the population of the level. Both monochromators are equipped for photon-counting, and the variation of detection efficiency with wavelength has been measured for each monochromator by comparison with a tungsten-ribbon lamp and with the luminescent efficiency of sodium salicylate. The levels are excited in a hollow-cathode discharge in argon. At a power level of 150 W, this source permits observation of lines with transition probability ≥ 10 5/sec. Our results are compared with recent measurements by a variety of methods at Harvard Observatory, Kiel, Air Force Cambridge Research Laboratory, and the National Bureau of Standards, as well as the 1969 compilation of Corliss and Tech. The new measurements are in good agreement, in so far as the limited overlap permits comparison, and disagree with the earlier values by roughly an order of magnitude. The new measurements indicate an error in the earlier values that increases with the excitation energy of the upper level. The new transition probabilities for Fe I imply a correspondingly higher solar iron abundance which has interesting consequences for solar models, the origin of meteorites, and solar neutrino production.