A mobile, coiled tubing drilling apparatus with a rotary drill head, includes a non-rotating mast on a mobile platform. The mast has mounted thereon an injector below a coiled tubing reel. The injector defines an operational axis for the coiled tubing. The rotary drill head is pivotally mounted on the injector so as to be movable between a retracted position away from the operational axis and an operating position in line with the operational axis. The rotary drill head includes a top swivel for non-rotating connection to the coiled tubing and a bottom spindle for rotating connection to a pipe section. The top swivel and the bottom spindle provide fluid communication between connected coiled tubing and connected pipe section during operation.