In my talk I will describe a construction, which answers the following question: given a triangulation of an oriented principal circle bundle P over a simplicial complex K (bundle projection is supposed to match the triangulations, i.e. it should be a simplicial map), find a  simplicial cochain in K, representing the Chern class of P. I will explain  the necessary definitions and if time permits describe briefly possible  generalizations of this construction. The talk is based on joint work with  N. Mnёv, POMI.