We report searches for the processes e(+) e(-) -> pi(+)pi(-)pi(0)chi(bJ) and e(+) e(-) -> phi chi(bJ) ( J = 1, 2) based on data samples collected by the Belle experiment at the KEKB collider. We report the first observation of the process e(+) e(-) -> (pi(+)pi(-)pi(0))non-omega(b1) and first evidence for e(+) e(-) -> omega chi(bJ) in the vicinity of the gamma(11020) resonance, with center- of- mass energies from 10.96 to 11.05 GeV. The significances for (pi(+)pi(-)pi(0))non-omega chi(b1) and omega chi(bJ) are greater than 5.3 sigma and 4.0 sigma, respectively. We also investigate the energy dependence of the e(+)e(-) -> (pi(+)pi(-)pi(0)) chi(bJ) cross section, but we cannot determine whether the contributions are from the gamma(10860) and gamma(11020) resonances or nonresonant continuum processes. The signals for e(+) e(-) ->phi chi(bj) are not significant, and the upper limits of the Born cross sections at the 90% confidence level are 0.7 and 1.0 pb for e(+)e(-) -> phi chi(bJ) and phi chi b(2), respectively, for center- of- mass energies from 10.96 to 11.05 GeV.