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Type Ia supernovae (SNe) serve as a fundamental pillar of modern cosmology, owing to their large luminosity and a well-defined relationship between light-curve shape and peak brightness. The precision distance measurements enabled by SNe Ia first revealed the accelerating expansion of the universe, now widely believed (though hardly understood) to require the presence of a mysterious "dark" energy. General consensus holds that Type Ia SNe result from thermonuclear explosions of a white dwarf (WD) in a binary system; however, little is known of the precise nature of the companion star and the physical properties of the progenitor system. Here we make use of extensive historical imaging obtained at the location of SN 2011fe/PTF11kly, the closest SN Ia discovered in the digital imaging era, to constrain the visible-light luminosity of the progenitor to be 10-100 times fainter than previous limits on other SN Ia progenitors. This directly rules out luminous red giants and the vast majority of helium stars as the mass-donating companion to the exploding white dwarf. Any evolved red companion must have been born with mass less than 3.5 times the mass of the Sun. These observations favour a scenario where the exploding WD of SN 2011fe/PTF11kly, accreted matter either from another WD, or by Roche-lobe overflow from a subgiant or main-sequence companion star., Comment: 22 pages, 6 figures, submitted