We present measurements of the charmonium state h(c) (P-1(1)) made with 106 x 10(6) psi' events collected by BESIII at BEPCII. Clear signals are observed for psi' -> pi(0)h(c) with and without the subsequent radiative decay h(c) -> gamma eta(c). First measurements of the absolute branching ratios B(psi' -> pi(0)h(c)) = (8.4 +/- 1.3 +/- 1.0 x 10(-4) and B(h(c) -> gamma eta(c)) = (54.3 +/- 6.7 +/- 5.2)% are presented. A statistics-limited determination of the previously unmeasured h(c) width leads to an upper limit Gamma(h(c)) pi(0)h(c)) x B(h(c) -> gamma eta(c)) = (4.58 +/- 0.40 +/- 0.50) x 10(-4) are consistent with previous results.
