B737 FLT CREW AT MDW EXPERIENCED A MOONEY OVERFLY WHILE TAXIING INTO POS FOR TKOF.

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I WAS THE CAPT ON FLT. WHILE HOLDING SHORT OF RWY 22L AT MDW; MY FO AND I HEARD THE TWR TELL ANOTHER CARRIER FLT THE ONLY ACFT ON FINAL WAS A MOONEY THAT'S CLRED TO LAND ON RWY 22R. I LOOKED UP AND SAW THE MOONEY ON ABOUT A 3 MI FINAL AND IT APPEARED TO BE LINED UP ON FINAL FOR RWY 22R. SHORTLY AFTER THAT; MDW TWR GAVE US CLRNC TO TAXI INTO POS AND HOLD RWY 22L. MY FO AND I NOTED TO EACH OTHER THAT THE MOONEY STILL APPEARED TO BE ON FINAL FOR RWY 22R; BUT ADMITTING LATER IT WAS HARD TO BE POSITIVE ABOUT IT BECAUSE THE FINALS FOR THE 2 RWYS ARE SO CLOSE TOGETHER. AS THE NOSE OF OUR ACFT CROSSED THE CTRLINE OF RWY 22L MY FO REALIZED THAT THE MOONEY WAS NOW LINED UP ON SHORT FINAL FOR OUR RWY 22L. I STOPPED THE ACFT AND THE FO XMITTED TO THE TWR THAT THE MOONEY WAS NOW LINED UP TO LAND ON RWY 22L. THE TWR CTLR; AFTER SOME CONFUSION; ASKED THE MOONEY IF HE WAS LNDG ON RWY 22R OR RWY 22L? THE MOONEY REPLIED THAT HE WAS LNDG RWY 22L AND; AS HE WAS TOUCHING DOWN; ASKED THE TWR IF THEY WANTED HIM TO GO AROUND. THE TWR CTLR AT THIS POINT SAID NO AND TO CLR THE RWY. MY FO AND I ESTIMATED THAT THE MOONEY FLEW DIRECTLY OVER US AT APPROX 75 FT. I FINISHED LINING UP ON RWY 22L AND WE TOOK OFF WITHOUT FURTHER INCIDENT. SUPPLEMENTAL INFO FROM ACN 599412: AS WE TAXI INTO POS ON RWY 22L WE OBSERVE THE MOONEY ON ABOUT A MI FINAL. WE COMPLETE THE BELOW-THE-LINE ITEMS ON THE CHKLIST AS WE ENTER THE RWY. I LOOKED UP AND SAW THE MOONEY ON SHORT FINAL. HIS LNDG LIGHTS LOOKED VERY CLOSE. I LOOKED DOWN AND REALIZED THAT OUR NOSE WAS ON THE CTRLINE; PERPENDICULAR TO THE RWY. I KNEW FOR SURE THAT HE WAS LINED UP WITH OUR RWY. I TOLD THE CAPT THAT HE WAS LNDG ON OUR RWY AND THE CAPT APPLIED THE BRAKES. I THEN TOLD THE TWR THAT THE MOONEY WAS LINED UP WITH RWY 22L. THE TWR RESPONDED THAT THE MOONEY IS LNDG ON RWY 22R. I THEN XMITTED THAT HE WAS RIGHT OVER US. THE CTLR POINTED OUT THE MOONEY PLT'S ERROR AS HE TOUCHED DOWN. WE WERE FORTUNATE THAT RWY 22L HAS A DISPLACED THRESHOLD AND THAT THE MOONEY PLT WAS FOLLOWING THE VASI; ALBEIT THE WRONG ONE. THE EXCHANGE BTWN ME; THE CTLR; AND THE MOONEY PLT WAS TIME CONSUMING AND; IN THE END; NOT VERY PRODUCTIVE. I THINK ONCE I REALIZED THAT HE WAS ON OUR RWY; I SHOULD HAVE JUST SAID; 'SEND THE MOONEY AROUND; HE'S ON OUR RWY.