LR31 FLT CREW MISTAKENLY RECORDS DEP ALT ASSIGNMENT AND VIOLATES ATC CLRNC WHILE DEPARTING MDW.

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THE FO WAS BUSY CLOSING THE DOOR AND BRIEFING THE PAX; SO I ELECTED TO CONTACT CLRNC DELIVERY MYSELF BEFORE HE WAS SEATED AND HAD HIS HEADSET ON. THE CLRNC DELIVERY CTLR READ OUR CLRNC VERY FAT; SO I COPIED AS FAST AS I COULD. WE WERE CLRED VIA THE MIDWAY 4 DEP (WHICH I COPIED IN SHORTHAND AS 'M 4'); MAINTAIN 3000 FT (WHICH I COPIED AS '3'). AFTER ENG START AND PWRING UP THE RADIOS; I REFERRED TO MY SHORTHAND CLRNC AND; SEEING MY SHORTHAND 'M 4;' PROGRAMMED THE ALT ALERTER FOR 4000 FT. ENG START AND TAXI WERE NORMAL. WHEN I BRIEFED THE FO; I REFERRED TO THE ALT ALERTER AND BRIEFED AN INITIAL ALT OF 4000 FT. OUR FIRST INDICATION OF A PROB WAS WHEN THE CTLR ASKED OUR ALT. WE RESPONDED THAT WE WERE LEVEL AT 4000 FT. NEXT; A DIFFERENT CTLR VOICE ASKED WHO HAD ASSIGNED US TO THAT ALT. WE RESPONDED THAT MIDWAY CLRNC DELIVERY HAS ASSIGNED US 4000 FT WHILE I CHKED MY SHORTHAND AND THE PRINTED DEP PROC CHART. WE REPEATED TO ATC THAT WE WERE LEVEL AT 4000 FT AND ASKED WHAT HE WANTED US TO DO. THE CTLR RESPONDED THAT WE WERE FINE AT 4000 FT. IN THE FUTURE; I WILL ALWAYS MAKE SURE THAT BOTH PLTS MONITOR THE CTLR WHEN WE RECEIVE OUR CLRNC AND BOTH PLTS WILL COMPARE THE CLRNC WITH THE PRINTED DEP PROC.