Using the semianalytic method proposed by Esmailzadeh and coworkers we calculate the abundances of the light elements produced during primordial nucleosynthesis assuming that the gauge coupling constants of the fundamental interactions may vary. We analyze the dependence of the nucleon masses, nuclear binding energies, and cross sections involved in the calculation of the abundances with the fundamental constants assuming the chiral limit of QCD. We obtain the abundances of light elements as a function of the fundamental constants. Finally, using the observational data of D, 3He, 4He, and 7Li, we estimate constraints on the variation of the fundamental constants between the time of primordial nucleosynthesis and the present. All observational abundances and the WMAP estimate of the baryon density can be fitted to the theoretical predictions with varying coupling constants. The possible systematic errors in the observational data preclude stronger conclusions.
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