Abstract: We point out that in the standard model there is meaningful quark mixing even in the extreme chiral (EC) limit, where only the third generation of quarks acquires mass. This mixing is in general expected to be of order 1 and the fact that |V-13|(2) + |V-23|(2) approximate to 1.6 x 10(-3) implies a novel fine-tuning problem in the SM which we point out for the first time. We propose a possible way of avoiding this fine-tuning by introducing a symmetry S which leads to V-CKM = 1, with only the third generation of quarks acquiring mass. We consider two scenarios for generating the mass of the first two quark generations and full quark mixing based on the assumption that the masses of the first two quark families are not generated by the standard Higgs. One consists of the introduction of a second Higgs doublet which is neutral under S. The second scenario consists of assuming new physics at a high energy scale, contributing to the masses of light quark generations, in an effective field theory approach. This last scenario leads to couplings of the Higgs particle to s (s) over bar and c (c) over tilde which are significantly enhanced with respect to those of the SM. In both schemes, one has scalar-mediated flavor-changing neutral currents which are naturally suppressed. Flavor-violating top decays are predicted in the second scenario at the level Br(t -> hc) >= 5 x 10(-5).