High spin states in the odd proton nucleus 129La have been investigated using the techniques of in-beam gamma -ray spectroscopy. Nine rotational bands have been observed in 129La, seven for the first time. Various band crossings were observed at rotational frequencies in the range h(cross) omega =0.28-0.57 MeV. The data are mainly discussed within the framework of the cranked shell model. The rotational bands are assigned quasiparticle configurations originating from pi h11/2, pi g7/2, pi (h11/2)2(X) pi g7/2 and pi 11/2 (X) nu (h11/2g7/2) states, respectively. Four of the band crossings are thought to be associated with the rotational alignments of the first pair of h11/2 neutrons or protons.