CARGO LTT TOOK OFF FROM A CLOSED RWY AT MDW CAUSING CONFLICT WITH GND EQUIPMENT.

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TO THE BEST OF OUR KNOWLEDGE; WE WERE GIVEN TAXI INSTRUCTION TO RWY 31L AT MDW. WE HAD JUST LANDED ON THAT SAME RWY 1 1/2 HRS EARLIER; SO WE DID NOT QUESTION THE INSTRUCTIONS; EVEN THOUGH THE ATIS INFO INDICATED RWY 31L WAS CLOSED. CONSIDERING THE TIME OF DAY; XA50; WE HAD FIGURED THE NEW ATIS INFO HAD NOT COME OUT YET. AS WE APCHED THE THRESHOLD OF RWY 31L WE NOTICED THE RWY LIGHTS WERE ON; WHICH CONFIRMED THE RWY WAS IN FACT OPEN. AFTER BEING GIVEN TKOF CLRNC ON RWY 31L; WE PROCEEDED AS NORMAL. AS THE ACFT REACHED ROTATION SPD MY F/O NOTICED A VAN APPROX 3000' DOWN THE RWY APPROX 500' OFF TO THE SIDE. THERE WAS NOT ANY OBSTRUCTION ON THE RWY. THIS WAS NOT AN UNCOMMON SIGHT; BECAUSE OF THE AMOUNT OF CONSTRUCTION THAT HAS BEEN UNDERWAY FOR THE LAST 3 MONTHS AT MDW. THE TKOF AND DEP WERE NORMAL; THE TWR CTLR TURNED US OVER TO DEP AND WE WENT ON OUR WAY. ON RETURN TO MDW 4 HRS LATER I HAD BEEN INFORMED THE CITY MAINT CREW HAD CONTACTED ATC TO FIND OUT WHO TOOK OFF RWY 31L WHEN IT WAS CLOSED; THE TWR CTLR EXPLAINED TO THE BEST OF HIS KNOWLEDGE NO ONE. I CALLED THE CTL TWR TO QUESTION THIS SERIES OF EVENTS. I WAS ADVISED THAT EVERYTHING WAS NORMAL. HE SAID THE CITY MAINT CREW HAD THOUGHT SOMEONE HAD TAKEN OFF ON A CLOSED RWY WHEN THAT WAS NOT THE CASE. THE CTLR ASKED THE CITY MAINT CREW TO IDENT THE AIRPLANE. THEY COULD NOT. THE ONLY THING THEY COULD TELL HIM WAS THE DEP TIME. THIS INCIDENT CAME AS A SHOCK TO ME; AS THE CTLR DID NOT CAUTION US AT ANY TIME RWY 31L WAS CLOSED. I FLY INTO MDW 8 TIMES/WK. I AM VERY FAMILIAR WITH THE AREA AS WELL AS THE CTLRS. DON'T LET THIS SECURITY BLANKET DECEIVE YOU. WHEN IN DOUBT QUESTION ALL THINGS. DON'T TAKE ANYTHING FOR GRANTED. SUPPLEMENTAL INFO FROM ACN 95853: NEAR MISS OCCURRED ON OR NEAR RWY 31L WHICH TWR RPTED CLOSED APPROX 50 MINS PRIOR TO OUR TKOF.