  We extract the proton charge radius from the elastic form factor (FF) data
using a novel theoretical framework combining chiral effective field theory and
dispersion analysis. Complex analyticity in the momentum transfer correlates
the behavior of the spacelike FF at finite $Q^2$ with the derivative at $Q^2 =
0$. The FF calculated in the predictive theory contains the radius as a free
parameter. We determine its value by comparing the predictions with a
descriptive global fit of the spacelike FF data, taking into account the
theoretical and experimental uncertainties. Our method allows us to use the
finite-$Q^2$ FF data for constraining the radius (up to $Q^2\sim$ 0.5 GeV$^2$
and larger) and avoids the difficulties arising in methods relying on the $Q^2
\rightarrow 0$ extrapolation. We obtain a radius of 0.844(7) fm, consistent
with the high-precision muonic hydrogen results.
