Models of the chemical evolution of the Milky Way suggest that the observed abundances of elements heavier than helium ('metals') require a continuous infall of gas with metallicity (metal abundance) about 0.1 times the solar value. An infall rate integrated over the entire disk of the Milky Way of approximately 1 solar mass per year can solve the 'G-dwarf problem'--the observational fact that the metallicities of most long-lived stars near the Sun lie in a relatively narrow range. This infall dilutes the enrichment arising from the production of heavy elements in stars, and thereby prevents the metallicity of the interstellar medium from increasing steadily with time. However, in other spiral galaxies, the low-metallicity gas needed to provide this infall has been observed only in associated dwarf galaxies and in the extreme outer disk of the Milky Way. In the distant Universe, low-metallicity hydrogen clouds (known as 'damped Ly alpha absorbers') are sometimes seen near galaxies. Here we report a metallicity of 0.09 times solar for a massive cloud that is falling into the disk of the Milky Way. The mass flow associated with this cloud represents an infall per unit area of about the theoretically expected rate, and approximately 0.1-0.2 times the amount required for the whole Galaxy.