CITATION CE560 FLT CREW HAS A TRACK HDG DEV DURING DEP FROM MDW.

Narrative

I WAS THE PF TAKING OFF ON RWY 22R OUT OF MDW. OUR INSTRUCTIONS WERE TO FLY THE MIDWAY 4 DEP OFF OF RWY 22R. OUR TKOF CLRNC OUT OF RWY 22R WAS TO EXECUTE A R TURN TO A HDG OF 110 DEGS WHILE CLBING TO 3000 FT MSL. AFTER LIFTOFF; WHEN I PROCEEDED TO EXECUTE THE R TURN TO THE ASSIGNED HDG OF 110 DEGS; THE CAPT QUESTIONED ME AND INFORMED ME THAT IT WAS TO BE A L TURN TO A HDG OF 110 DEGS. I DISAGREED WITH HIM; BUT WE BOTH FAILED TO CONFIRM WITH MIDWAY TWR AND I PROCEEDED TO MAKE THE L TURN TO A HDG OF 110 DEGS. ONCE THE TWR CTLR REALIZED THAT WE WERE ON A L TURN; HE INSTRUCTED US TO IMMEDIATELY EXECUTE A R TURN TO THE PREVIOUSLY ASSIGNED HDG OF 110 DEGS. I IMMEDIATELY CORRECTED THE DEV AND EXECUTED THE R TURN TO THE ASSIGNED HDG. THERE WERE NO FURTHER QUERIES FROM THE CTLR. IT WAS A PARTICULARLY BUSY NIGHT AT MIDWAY THAT DAY; LOW VISIBILITY AND RAIN PREVAILED AND THE WX HAD AN IMPACT ON DELAYING ARRS AND DEPS. I BELIEVE THAT OPERATING UNDER THOSE CONDITIONS CAN BE CHALLENGING AND STRESSFUL TO ANY PLT; THUS CONTRIBUTING TO OUR MISTAKE. I ALSO BELIEVE THAT NOT CONFIRMING WITH THE CTLR BEFORE DECIDING TO MAKE THE L TURN WAS DEFINITELY A COM BREAKDOWN ON OUR PART.