We measured the g(1) spin structure function of the deuteron at low Q(2), where QCD can be approximated with chiral perturbation theory (chi PT). The data cover the resonance region, up to an invariant mass of W approximate to 1.9 GeV. The generalized Gerasimov-Drell-Hearn sum, the moment Gamma(d)(1) and the spin polarizability gamma(d)(0) are precisely determined down to a minimum Q(2) of 0.02 GeV2 for the first time, about 2.5 times lower than that of previous data. We compare them to several chi PT calculations and models. These results are the first in a program of benchmark measurements of polarization observables in the chi PT domain.