We present a new type of 3D printer that can form precise, but soft and deformable 3D objects from layers of off-the-shelf fabric. Our printer employs an approach where a sheet of fabric forms each player of a 3D object. The printer cuts this sheet along the 2D contour of the layer using a laser cutter and then bonds it to previously printed layers using a heat sensitive adhesive. Surrounding fabric in each layer is temporarily retained to provide a removable support structure for layers printed above it. This process is repeated to build up a 3D object layer by layer. Our printer is capable of automatically feeding two separate fabric types into a single print. This allows specially cut layers of conductive fabric to be embedded in our soft prints. Using this capability we demonstrate 3D models with touch sensing capability built into a soft print in one complete printing process, and a simple LED display making use of a conductive fabric coil for wireless power reception.