B737 DEPARTING MDW EXPERIENCED UNCERTAINTY WITH ATC ASSIGNED ALT.

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CAPT'S LEG; WE WERE CLBING OUT SHORTLY AFTER DEPARTING FROM MDW; WHEN CHICAGO DEP TOLD US TO 'TURN R TO 250 DEGS; CLB TO 7000 FT.' I REPLIED WITH THE PROPER RESPONSE; AND THE CAPT BEGAN MOVING THE JET PER THAT INSTRUCTION. PASSING THROUGH APPROX 5500 FT; THE CAPT ASKED ME TO QUERY DEP TO CONFIRM 7000 FT. I DID; AND IMMEDIATELY THE CTLR REPLIED; 'NEGATIVE; 5000 FT; TURN R IMMEDIATELY TO 320 DEGS; CLB TO 6000 FT; YOU HAVE TFC AT YOUR 1 O'CLOCK POS; AND NEED TO TURN NOW.' WE IMMEDIATELY SPOTTED THE TFC AT APPROX 5+ MI AWAY; TURNED TO THE HEADING; KNOWING THIS HEADING WOULD CLR US BEHIND THAT TFC. THE CTLR THEN TOLD US TO CLB TO 12000 FT; AND TO CONFIRM WE HAD A VISUAL WITH THE TFC. WE DID AND RESPONDED ONCE AGAIN. THE CTLR NEVER SAID ANYTHING FURTHER ABOUT THE CONFLICT; GAVE US ANOTHER VECTOR ONCE LEVEL AT 12000 FT; AND ROUTINELY SENT US TO ZAU TO CONTINUE OUR DEP. BOTH THE CAPT AND I BELIEVED THE CTLR HAD INITIALLY GIVEN US A 7000 FT INITIAL CLRNC; AND THAT I HAD READ THAT ALT BACK TO HIM. I THINK THE CTLR MEANT TO SAY 270 DEGS AND 5000 FT; VERSUS 250 DEGS AND 7000 FT WHICH THE CAPT AND I BELIEVED WE HEARD HIM SAY. UPON FURTHER DISCUSSION; THE CAPT HAD ASKED ME TO QUERY THE CTLR DURING THE CLB DUE TO THE UNIQUE ALT (7000 FT) GIVEN TO US FOR AN INTERMEDIATE ALT ON A TYPICAL DEP FROM MDW. THE ACFT WE TURNED AWAY FOR NEVER GOT CLOSER THAN 3-5 MI.