AIR CARRIER FLC INVOLVED IN NON-ESSENTIAL CONVERSATION TAKES WRONG TXWY AND EXPERIENCES MINOR RWY INCURSION. NO CONFLICT RESULTS.

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WHILE TAXIING TO RWY 01 AFTER RECEIVING CLRNC; I MISREAD TAXI SIGNS. BELIEVING I WAS ON ALPHA CROSSING RWY 32 AS DIRECTED; I FOUND MYSELF AT THE CONVERGING POINT OF THE THREE RWYS. IT WAS LATE; WITHOUT OTHER TFC IN THE AREA; SO GROUND SIMPLY DIRECTED US TO TURN AROUND TAXI BACK AND GO TO THE NEXT INTERSECTION. I HAD TURNED ONE TOO SOON. MY MISTAKE WAS COMPLACENCY IN A VERY FAMILIAR ARPT AND ALLOWING NON-ESSENTIAL TALK IN A CRITICAL PHASE. I WAS LUCKILY THERE WAS NO TFC DUE TO THE LATE HOUR; BUT THIS SHOULD NEVER HAVE HAPPENED. I GOT A FREE WAKE UP CALL. CALLBACK CONVERSATION WITH RPTR REVEALED HE FOLLOWING INFO: RPTR NOTED THAT THE ACFT JUST CROSSED THE HOLD SHORT LINE; BUT DID NOT ACTUALLY PENETRATE THE RWY. REPORTED FURTHER NOTED THAT CREW FATIGUE MAY HAVE BEEN A FACTOR-ALTHOUGH SHE HAD BEEN ON DUTY 5 HOURS; THE FO HAD BEEN ON DUTY FOR SOMEWHAT MORE THAN 10 HOURS. THE CTLR WAS WORKING COMBINED POSITIONS; INCLUDING GND; LOCAL AND CTLR WAS WORKING COMBINED POSITIONS; INCLUDING GND; LOCAL AND DEPARTURE; AND ALERTED THE CREW OF THEIR ERROR AT THE SAME TIME THE CREW RECOGNIZED THE DEVIATION.