  We present a measurement of the top-quark pair production cross-section in
proton-antiproton collisions at $\sqrt{s}$=1.96 TeV. The data were collected at
the Fermilab Tevatron by the CDF II detector and correspond to an integrated
luminosity of 8.8 fb$^{-1}$, representing the complete CDF Run II data set. We
select events consistent with the production of top-quark pairs by requiring
the presence of two reconstructed leptons, an imbalance in the total event
transverse momentum, and jets. At least one jet is required to be identified as
consistent with the fragmentation of a bottom quark using a
secondary-vertex-finding algorithm. The 246 candidate events are estimated to
have a signal purity of 91%. We measure a cross section of $\sigma_{\ttbar}$ =
7.09 $\pm$ 0.84 pb, assuming a top-quark mass of 172.5 GeV/$c^{2}$. The results
are consistent with the standard model as predicted by next-to-leading-order
calculations.
