DURING CLIMBOUT AFTER TAKEOFF, THE PILOT EXPERIENCED AN ENGINE FIRE AND DIVERTED TO CHICAGO'S MIDWAY AIRPORT FOR AN EMERGENCY LANDING. THE PILOT EXECUTED EMERGENCY PROCEDURES, SHUT DOWN THE ENGINE, THE FUEL SUPPLY, AND ALL ELECTRICAL LOAD. WHEN THE PILOT KNEW HE HAD THE RUNWAY MADE, HE SELECTED THE GEAR DOWN POSITION WITH THE GEAR HANDLE, BUT ELECTED NOT TO VERIFY GEAR DOWN AND LOCKED FOR SAFETY REASONS. THE GEAR FAILED TO EXTEND; A GEAR UP LANDING ENSUED. IT WAS REPORTED THAT THE LANDING GEAR WOULD DROP WHEN THE GEAR HANDLE WAS ACTIVATED. POST-ACCIDENT EXAMINATION OF THE ENGINE COMPARTMENT REVEALED THAT THE FIRE WAS THE RESULT OF A LOOSE LINE FITTING ON A FUEL INJECTOR NOZZLE WHICH ALLOWED RAW FUEL TO SPRAY INTO THE COMPARTMENT; SPECIFICALLY, ONTO THE TURBO-CHARGER. THE AIRCRAFT WAS JACKED UP AND REMOVED FROM THE RUNWAY BEFORE AN INVESTIGATOR ARRIVED ON THE SCENE.