The Sun's internal rotation Ω(r,Θ) has previously been measured using helioseismology techniques and found to be a complex function of colatitude θ and radius r. From helioseismology and observations of apparently "rooted" solar magnetic tracers, we know that the surface rotates more slowly than much of the interior. The cause of this slow-down is not understood, but it is important for understanding stellar rotation generally and any plausible theory of the solar interior. A new analysis using 5-min solar p-mode limb oscillations as a rotation "tracer" finds an even larger velocity gradient in a thin region at the top of the photosphere. This shear occurs where the solar atmosphere radiates energy and angular momentum. We suggest that the net effect of the photospheric angular momentum loss is similar to Poynting-Robertson "photon braking" on, for example, Sun-orbiting dust. The resultant photospheric torque is readily computed and, over the Sun's lifetime, is found to be comparable to the apparent angular momentum deficit in the near-surface shear layer.