This case can be printed as one piece. The parts will print with some supports in the hinging mechanism, but these can be broken quite easily leaving you with a smoothly turning hinge.

In order to reduce supports required and optimize the functionality of the hinge, I would recommend printing the case with the side of the case against the printer bed (not the top or bottom faces) and with the case opened to about 45 degrees. This will hopefully give you the results you are looking for. Best of luck!