  We determine the root-mean-square proton charge radius, $R_{\rm p}$, from a
fit to low-$Q^2$ electron-proton elastic scattering cross section data with the
higher moments fixed (within uncertainties) to the values predicted by chiral
perturbation theory. We obtain $R_{\rm p}=0.857(11)$ fm. This number falls
between the value obtained from muonic hydrogen analyses and the CODATA value
(based upon atomic hydrogen spectroscopy and electron-proton scattering
determinations).
