  We study the impact on the primordial abundances of light elements created by
a variation of the quark masses at the time of Big Bang nucleosynthesis (BBN).
In order to navigate through the particle and nuclear physics required to
connect quark masses to binding energies and reaction rates in a
model-independent way, we use lattice QCD data and a hierarchy of effective
field theories. We find that the measured Helium-4 abundances put a bound of -1
% <~ d m_q/m_q <~ 0.7 % on a possible variation of quark masses. The effect of
quark mass variations on the deuterium abundances can be largely compensated by
changes of the baryon-to-photon ratio eta. Including bounds on the variation of
eta coming from WMAP results and adding some additional assumptions further
narrows the range of allowed values of d m_q/m_q.
