  The oscillation results published by the Double Chooz collaboration in 2011
and 2012 rely on background models substantiated by reactor-on data. In this
analysis, we present a background-model-independent measurement of the mixing
angle $\theta_{13}$ by including 7.53 days of reactor-off data. A global fit of
the observed neutrino rates for different reactor power conditions is
performed, yielding a measurement of both $\theta_{13}$ and the total
background rate. The results on the mixing angle are improved significantly by
including the reactor-off data in the fit, as it provides a direct measurement
of the total background rate. This reactor rate modulation analysis considers
antineutrino candidates with neutron captures on both Gd and H, whose
combination yields $\sin^2(2\theta_{13})=$ 0.102 $\pm$ 0.028(stat.) $\pm$
0.033(syst.). The results presented in this study are fully consistent with the
ones already published by Double Chooz, achieving a competitive precision. They
provide, for the first time, a determination of $\theta_{13}$ that does not
depend on a background model.
