  We obtain a model independent expression for the muonic hydrogen Lamb shift.
This expression includes the leading logarithmic ${\cal O}(m_{\mu}\alpha^6)$
terms, as well as the leading ${\cal O}(m_{\mu}\alpha^5
\frac{m_{\mu}^2}{m_{\rho}^2})$ hadronic effects. The latter are controlled by
the chiral theory, which allows for their model independent determination. In
this paper we give the missing piece for their complete expression including
the pion and Delta particles. Out of this analysis and the experimental
measurement of the muonic hydrogen Lamb shift we determine the electromagnetic
proton radius: $r_p=0.8412(15)$ fm. This number is at 6.8$\sigma$ variance with
respect to the CODATA value. The accuracy of our result is limited by
uncomputed terms of ${\cal
O}(m_{\mu}\alpha^5\frac{m_{\mu}^3}{m_{\rho}^3},m_{\mu}\alpha^6)$. This
parametric control of the uncertainties allows us to obtain a model independent
determination of the error, which is dominated by hadronic effects.
