I have a 1938 house. Most of it has had the wiring upgraded. However, I have one room with multiple outlets that are all ungrounded with the original cloth covered wiring. There is only one pair of wires (1 black, 1 white) coming out of each outlet on the circuit. I want to add a single GFCI outlet to the first receptacle in the circuit to provide ground fault protection to it and all the other outlets downstream. But can I do this by simply connecting the single pair of wires in the first outlet to the the GFCI Line connectors? I don't see how this would work to break the circuit downstream if there there aren't two pairs of wires available (a pair of Load and a pair of Line wires) to hook up to the GFCI outlet. I really don't want to mess with or modify any of the the old wiring.
If it isn't possible to protect the entire branch with a single GFCI outlet, would I just be better off installing a GFCI breaker that serves that branch?