Narrative:

Our initial clearance from clearance delivery was as follows: midway 4 departure; as filed; climb and maintain 3000 ft; departure 133.5; squawk XXXX. I read this back and was told readback correct. We taxied to runway 22R. Our clearance for takeoff was as follows: cleared for takeoff runway 22R; full length; right turn to 250 degrees. That's what I read back. We took off; turned to a heading of 250 degrees and were just passing 2000 ft when I noticed on the TCAS an aircraft approximately 2-3 mi; 12 O'clock position; and 400-500 ft above. I notified the PF to descend. As we were doing this; tower told us to maintain 2000 ft. We did and the other aircraft passed above at 400-500 ft. Tower said he issued 2000 ft as a clearance; but neither I nor the PF recall that; or read that back before takeoff. Prior to this; a citation took off before us with clearance of a right turn to 100 degrees. They went left and tower was frantically trying to get them to turn right. We believe that was the aircraft that came close to us circling back in the direction they were supposed to go. Also; there seemed to be some confusion on the tower's part on which aircraft he was talking to. We think tower was trying to tell the aircraft that came close to us to stay at 2000 ft but using the wrong tail number as an aircraft waiting to depart after us said; 'we are on the ground yet; you must mean the other aircraft.' we both believe that we flew the clearance given us.

Related reports:

Google
 

Original NASA ASRS Text

Title: PREMIER 1A FLT CREW HAS A TCAS ALERT DURING DEP FROM MDW.

Narrative: OUR INITIAL CLRNC FROM CLRNC DELIVERY WAS AS FOLLOWS: MIDWAY 4 DEP; AS FILED; CLB AND MAINTAIN 3000 FT; DEP 133.5; SQUAWK XXXX. I READ THIS BACK AND WAS TOLD READBACK CORRECT. WE TAXIED TO RWY 22R. OUR CLRNC FOR TKOF WAS AS FOLLOWS: CLRED FOR TKOF RWY 22R; FULL LENGTH; R TURN TO 250 DEGS. THAT'S WHAT I READ BACK. WE TOOK OFF; TURNED TO A HDG OF 250 DEGS AND WERE JUST PASSING 2000 FT WHEN I NOTICED ON THE TCAS AN ACFT APPROX 2-3 MI; 12 O'CLOCK POS; AND 400-500 FT ABOVE. I NOTIFIED THE PF TO DSND. AS WE WERE DOING THIS; TWR TOLD US TO MAINTAIN 2000 FT. WE DID AND THE OTHER ACFT PASSED ABOVE AT 400-500 FT. TWR SAID HE ISSUED 2000 FT AS A CLRNC; BUT NEITHER I NOR THE PF RECALL THAT; OR READ THAT BACK BEFORE TKOF. PRIOR TO THIS; A CITATION TOOK OFF BEFORE US WITH CLRNC OF A R TURN TO 100 DEGS. THEY WENT L AND TWR WAS FRANTICALLY TRYING TO GET THEM TO TURN R. WE BELIEVE THAT WAS THE ACFT THAT CAME CLOSE TO US CIRCLING BACK IN THE DIRECTION THEY WERE SUPPOSED TO GO. ALSO; THERE SEEMED TO BE SOME CONFUSION ON THE TWR'S PART ON WHICH ACFT HE WAS TALKING TO. WE THINK TWR WAS TRYING TO TELL THE ACFT THAT CAME CLOSE TO US TO STAY AT 2000 FT BUT USING THE WRONG TAIL NUMBER AS AN ACFT WAITING TO DEPART AFTER US SAID; 'WE ARE ON THE GND YET; YOU MUST MEAN THE OTHER ACFT.' WE BOTH BELIEVE THAT WE FLEW THE CLRNC GIVEN US.

Data retrieved from NASA's ASRS site as of January 2009 and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.