The tangle-free, kink-free oxygen supply extensible tubing uses a helical accordion support structure on which the oxygen supply tubing is attached. The helical accordion backbone has some tendency to spring back, but this is not relied upon to extend and return the oxygen supply tubing it carries. The carrier structure keeps the oxygen tubing from getting tangle or kinked. A centrally located retractable line, which is located within the center of the helical accordion structure, acts as the retracting mechanism, as it tends to allow the accordion structure to be pulled into an extended position, while upon rewinding the central cord, the helical accordion support structure can be pushed toward a collapsed position without the oxygen supply line tubing becoming tanked, kinked, and thereby blocked. As a safety feature , so the oxygen line does not encounter and strain between it and the patient, a chest-harness has attachment to the helical accordion support structure.