A particle rotor model (PRM) with a quasi-proton and a quasi-neutron coupled with a triaxial rotor is developed and applied to study chiral doublet bands with configurations of a h 11/2 proton and a h 11/2 quasi-neutron. With pairing treated by the BCS approximation, the present quasiparticle PRM is aimed at simulating one proton and many neutron holes coupled with a triaxial rotor. After a detailed analysis of the angular momentum orientations, energy separation between the partner bands, and behavior of electromagnetic transitions, for the first time we find aplanar rotation or equivalently chiral geometry beyond the usual one proton and one neutron hole coupled with a triaxial rotor.