  We measured two-neutrino double beta decay of $^{130}$Te using an exposure of
300.7 kg$\cdot$yr accumulated with the CUORE detector. Using a Bayesian
analysis to fit simulated spectra to experimental data, it was possible to
disentangle all the major background sources and precisely measure the
two-neutrino contribution. The half-life is in agreement with past measurements
with a strongly reduced uncertainty: $T^{2\nu}_{1/2} =
7.71^{+0.08}_{-0.06}\mathrm{(stat.)}^{+0.12}_{-0.15}\mathrm{(syst.)}\times10^{20}$
yr. This measurement is the most precise determination of the $^{130}$Te
2$\nu\beta\beta$ decay half-life to date.
