The spectral breadth of conjugated polymers gives these materials a clear advantage over other molecular compounds for organic photovoltaic applications and is a key factor in recent efficiencies topping 10%. However, why do excitonic transitions, which are inherently narrow, lead to absorption over such a broad range of wavelengths in the first place? Using single-molecule spectroscopy, we address this fundamental question in a model material, poly(3-hexylthiophene). Narrow zero-phonon lines from single chromophores are found to scatter over 200 nm, an unprecedented inhomogeneous broadening that maps the ensemble. The giant red shift between solution and bulk films arises from energy transfer to the lowest-energy chromophores in collapsed polymer chains that adopt a highly ordered morphology. We propose that the extreme energetic disorder of chromophores is structural in origin. This structural disorder on the single-chromophore level may actually enable the high degree of polymer chain ordering found in bulk films: both structural order and disorder are crucial to materials physics in devices.