B777 CREW MISSES SID ALT RESTRS WHEN DISTRACTED BY A TCASII TA.

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OUR CLRNC FROM ORD WAS THE ORD 1 DEP. WE DEPICTED THE 5 AND 8 DME RINGS ON OUR FMS TO HELP US WITH THE XING RESTRS. WE WERE THEN CLRED. THE FO TOOK OFF FROM RWY 32R WITH A R TURN TO 020 DEGS. SHORTLY AFTER ROLLING OUT ON OUR ASSIGNED HEADING WE RECEIVED A TA WITH ONLY A YELLOW DOT ON OUR TCASII DISPLAY; MEANING NO ALT INFO. AT THIS TIME; ALL 3 PLTS LOOKED OUTSIDE FOR THE TFC. IN DOING SO; OUR CLB WAS INADVERTENTLY SLOWED AND WE BRIEFLY IGNORED OUR ALT MINIMUM FOR THE 5 DME POS. DEP ASKED IF WE INFORMED ANYONE THAT WE WERE UNABLE TO MEET THE XING RESTR. I ANSWERED; 'NO.' HE SAID WE MISSED OUR ALT RESTR BY 500 FT. OUR DATA INDICATED THAT WE WERE 200 FT BELOW THE 3000 FT RESTR. NONETHELESS WE WERE BELOW THE REQUIRED ALT. I WILL BE SURE IN THE FUTURE THAT THE PF WILL CONCENTRATE SOLELY ON FLYING THE ACFT AND COMPLYING WITH ALL RESTRS. SUPPLEMENTAL INFO FROM ACN 467189: THE DISTR OF THE TCASII EVENT HAD DRAWN MY ATTN FROM THE SID. ALSO I WAS COMPLACENT DUE TO NEVER HAVING A PROB MAKING THE RESTR ON THE B777 DURING THE WINTER MONTHS. SUPPLEMENTAL INFO FROM ACN 467191: OUR WT WAS SUCH THAT WE COULD HAVE COMPLIED WITH THE REQUIREMENT ABSENT UNUSUAL CIRCUMSTANCES; BUT WITHOUT MUCH MARGIN FOR ERROR. THE TFC ALERT WAS THE IMMEDIATE DISTR; BUT WITH HINDSIGHT WE SHOULD HAVE REQUESTED RELIEF FROM THE ALT RESTR; BECAUSE OF THE GREATER FLEXIBILITY AND MARGIN FOR ERROR IT WOULD HAVE ALLOWED IN THIS SIT.