The recent work of J. Tits [4] on local characterizations of building introduces the important new concept of chamber system and its ramified covers, and it is the purpose of this paper to present a systematic and elementary development of the basic results on ramified covers of chamber systems. This has applications to Buekenhout's work [1] on diagram geometries, whose connection with chamber systems is explained in [4]. After some preliminary definitions and lemmas in Section 1, we introduce in Section 2 two types of complexes associated with a chamber system. If the chamber system {ie259-1} has finite rank it is equivalent to a certain type of regular cell complex {ie259-2}, which in special cases is a building, see [4]. We also introduce some 2-dimensional simplicial complexes {ie259-3}, topological covers of which corresponds to {ie259-4}-covers of the chamber system. Sections 3–6 deals with the elementary theoery of {ie259-5}-covers without assuming any prior knowledge of topology; the proofs of the results are short and straightforward, so there is little to be gained by the less direct method of using known topological results for {ie259-6}. Section 7 deals with automorphisms; we give necessary and sufficient conditions for an automorphism of {ie259-7} to lift to an automorphism of some {ie259-8}-cover {ie259-9}, and we show that if the covering is characteristic, the Aut {ie259-10} lifts to a section of Aut {ie259-11}. Finally I should like to make it quite clear that many concepts and definitions in this paper (e.g. chamber system, galleries, m-covers, elementary homotopy) are due to J. Tits [4], and I would like to thank him for several helpful discussion at Santa Cruz. The reader should refer to Tits' work in [4] for motivation, relationships with combinatorial geometries, and the beautiful characterization of buildings given therein.