Narrative:

While being radar vectored for mdw, level 4000', 180 degree heading, ATC called VFR traffic at 1 O'clock and 3 mi level, 3500' unconfirmed. A few moments later ATC called the traffic 2 O'clock and 1 mi climbing. My first officer and I had no visibility contact with the traffic, of which we promptly informed the approach controller. At that time the controller stated, 'this is a traffic alert, suggest immediate climb.' during the climb my first officer saw an small transport pass under our aircraft, climbing and deviating off its east heading to the north. The aircraft may have seen us at the last minute and deviated to avoid a conflict.

Google
 

Original NASA ASRS Text

Title: SMT AT CRUISE ON VECTORS TO MDW HAD NMAC WITH ANOTHER SMT. EVASIVE ACTION TAKEN TO AVOID COLLISION.

Narrative: WHILE BEING RADAR VECTORED FOR MDW, LEVEL 4000', 180 DEG HDG, ATC CALLED VFR TFC AT 1 O'CLOCK AND 3 MI LEVEL, 3500' UNCONFIRMED. A FEW MOMENTS LATER ATC CALLED THE TFC 2 O'CLOCK AND 1 MI CLBING. MY F/O AND I HAD NO VIS CONTACT WITH THE TFC, OF WHICH WE PROMPTLY INFORMED THE APCH CTLR. AT THAT TIME THE CTLR STATED, 'THIS IS A TFC ALERT, SUGGEST IMMEDIATE CLB.' DURING THE CLB MY F/O SAW AN SMT PASS UNDER OUR ACFT, CLBING AND DEVIATING OFF ITS E HDG TO THE N. THE ACFT MAY HAVE SEEN US AT THE LAST MINUTE AND DEVIATED TO AVOID A CONFLICT.

Data retrieved from NASA's ASRS site as of August 2007 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.