The tau(-) -> eta pi(-) pi(+) pi(-) nu(tau) decay with the eta -> gamma gamma mode is studied using 384 fb(-1) of data collected by the BABAR detector. The branching fraction is measured to be (1.60 +/- 0.05 +/- 0.11) x 10(-4). It is found that tau(-) -> f(1) (1285) pi(-)nu(tau) -> eta pi(-) pi(+) pi(-) nu(tau) is the dominant decay mode with a branching fraction of (1.11 +/- 0.06 +/- 0.05) x 10(-4). The first error on the branching fractions is statistical and the second systematic. Note that no particle identification algorithm is applied to the charged tracks to distinguish pions from kaons. In addition, a 90% confidence level upper limit on the branching fraction of the tau(-) -> eta(')(958)pi(-) nu(tau) decay is measured to be 7.2 x 10(-6). This last decay proceeds through a second-class current and is expected to be forbidden in the limit of isospin symmetry.