The proton burning process p + p --> d + e(+) + nu(e), important for the st
ellar evolution of main-sequence stars of mass equal to or less than that o
f the Sun, is computed in effective field theory by means of chiral perturb
ation expansion to the next to next to leading chiral order. This represent
s a model-independent calculation consistent with low-energy effective theo
ry of QCD comparable in accuracy to the radiative np capture at thermal ene
rgy previously calculated by first using very accurate two-nucleon wave fun
ctions backed up by an effective held theory technique with a finite cutoff
. The result obtained thereby is found to support within theoretical uncert
ainties the previous calculation of the same process by Bahcall and his cow
orkers.