  The sixth-order electron-loop vacuum-polarization contribution to the
$2P_{1/2} - 2S_{1/2}$ Lamb shift of the muonic hydrogen ($\mu^{-} p^+$ bound
state) has been evaluated numerically. Our result is 0.007608(1) meV. This
eliminates the largest uncertainty in the theoretical calculation. Combined
with the proposed precision measurement of the Lamb shift it will lead to a
very precise determination of the proton charge radius.
