A jaw displacement oral appliance to be inserted in the mouth of a user to adjust the position of the user's lower jaw relative to the user's upper jaw so as to maintain an open airway to the user's throat through which the user can breathe while sleeping, said oral appliance comprising: an upper arch tray assembly having an upper tooth impression liner configured to receive an upper set of teeth of the user's upper jaw during sleep; a lower arch tray assembly having a lower tooth impression liner configured to receive a lower set of teeth of the user's lower jaw during sleep; an intermediate arch tray assembly lying between said upper and said lower arch tray assemblies and being attached to said lower arch tray assembly, and each of said upper, said intermediate and said lower arch tray assemblies having a pair of sides that are spaced from and lie opposite one another; and a coupler; the jaw displacement oral appliance characterized in that the coupler being connected to and extending downwardly from each of the pair of sides of said upper arch tray assembly and being pivotally coupled to respective ones of the pair of sides of said intermediate arch tray assembly, whereby said upper and said intermediate arch tray assemblies are pivotally connected together and said upper arch tray assembly is rotatable at said couplers with the user's upper set of teeth to pivot upwardly relative to said intermediate arch tray assembly so as to move in a vertical first direction away from said lower arch tray assembly and the user's lower set of teeth when the user's mouth is opened during sleep, said lower arch tray assembly being attached to said intermediate arch tray assembly such that said lower arch tray assembly is adapted to move back and forth with the user's lower set of teeth in a horizontal second direction relative to each of said intermediate arch tray assembly and said upper arch tray assembly that is pivotally connected to said intermediate arch tray assembly, whereby to correspondingly adjust the position of the user's lower jaw relative to the position of the user's upper jaw. an upper arch tray assembly having an upper tooth impression liner configured to receive an upper set of teeth of the user's upper jaw during sleep; a lower arch tray assembly having a lower tooth impression liner configured to receive a lower set of teeth of the user's lower jaw during sleep; an intermediate arch tray assembly lying between said upper and said lower arch tray assemblies and being attached to said lower arch tray assembly, and each of said upper, said intermediate and said lower arch tray assemblies having a pair of sides that are spaced from and lie opposite one another; and a coupler; the jaw displacement oral appliance characterized in that the coupler being connected to and extending downwardly from each of the pair of sides of said upper arch tray assembly and being pivotally coupled to respective ones of the pair of sides of said intermediate arch tray assembly, whereby said upper and said intermediate arch tray assemblies are pivotally connected together and said upper arch tray assembly is rotatable at said couplers with the user's upper set of teeth to pivot upwardly relative to said intermediate arch tray assembly so as to move in a vertical first direction away from said lower arch tray assembly and the user's lower set of teeth when the user's mouth is opened during sleep, said lower arch tray assembly being attached to said intermediate arch tray assembly such that said lower arch tray assembly is adapted to move back and forth with the user's lower set of teeth in a horizontal second direction relative to each of said intermediate arch tray assembly and said upper arch tray assembly that is pivotally connected to said intermediate arch tray assembly, whereby to correspondingly adjust the position of the user's lower jaw relative to the position of the user's upper jaw.