Define a chordally signed graph to be a signed chordal graph (meaning that each edge is designated as being positive or negative and every induced cycle is a triangle) in which every positive cycle C (meaning every cycle C that contains an even number of negative edges) has a chord e such that C {e} forms two positive cycles. Two characterizations of chordally signed graphs support the naturalness of this definition. In addition, chordally signed graphs can be easily recognized when the underlying graph has at most two maximal complete subgraphs (with minimal balancing vertex sets playing a key role).