The decay tau(-) --> K- eta nu(tau), has been observed with the CLEO I
I detector. The eta meson is reconstructed using two decay channels, e
ta --> gamma gamma and pi(+)pi(-)pi(0). The measured branching fractio
n is B(tau(-) --> K- eta nu(tau)) = (2.6 +/- 0.5 +/- 0.4) x 10(-4), so
mewhat higher than theoretical estimates. An improved upper limit for
the second-class-current decay tau(-) --> pi(-) eta nu(tau) is set, B(
tau(-) --> pi(-) eta nu(tau)) < 1.4 x 10(-4) at 95% C.L., consistent w
ith theoretical expectations.