DIVERSION TO ALTERNATE IN ACR WDB ACFT. MEDICAL EMER WITH ILL PAX. FLC FAILED TO GET A RELEASE FROM DISPATCHER.

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AT APPROX XA15Z THE LEAD FLT ATTENDANT INFORMED THE COCKPIT CREW THAT WE HAD A PAX EXPERIENCING CHEST PAINS AND THAT THEY HAD PAGED AND FOUND A DOCTOR. A FEW MINS LATER SHE RETURNED TO THE COCKPIT AND MENTIONED THAT THE DOCTOR ATTENDING HE PAX WAS A CARDIOLOGIST AND THAT HE WAS REQUESTING THE EMER MEDICAL KIT; WHICH WAS THEN HANDED TO HER BY THE SO. AT THAT PINT; WE NOTICED WE WERE APPROX 170 NM NE OF BIL JUST IN CASE IT WAS NECESSARY TO LAND SOMEWHERE SOON WHERE THE ILL PAX COULD BE DEPLANED AND TAKEN TO THE HOSPITAL. AFTER ABOUT 10 MORE MINS HAD PASSED; THE LEAD FLT ATTENDANT INFORMED US THAT THE DOCTOR RECOMMENDED WE LAND AS SOON AS POSSIBLE. WE WERE THEN ABOUT 100 NM NNE OF BIL WHERE WE ASKED FOR AND RECEIVED A CLRNC TO BIL FROM ZLC. WE IMMEDIATELY STARTED A L TURN TOWARDS BIL AND A DSCNT FROM FL350. I INFORMED THE PAX OF OUR DIVERSION AND THEN MENTIONED TO THE FO AND SO THAT WE SHOULD CALL DISPATCH TO LET THEM KNOW; BUT THEN WE ALL AGREED THAT THERE WAS NOT ENOUGH TIME TO TALK TO DISPATCH AT THAT POINT. MINS LATER WE MADE A VISUAL APCH TO RWY 10L AT BIL AND WERE PARKED ON THE RAMP AT XB10Z. PARAMEDICS BOARDED THE ACFT AND REMOVED THE ILL PAX AND THE PAX'S WIFE ALSO DEPLANED. DISPATCH WAS CALLED; FUEL WAS ADDED; A NEW FLT PLAN AND RELEASE WAS RECEIVED AND WE DEPARTED BIL AT XC09Z FOR SEA. THE 3 OF US IN THE COCKPIT FELT THAT EVERYTHING HAD GONE QUITE WELL; THOUGH DISPATCH WAS NOT VERY PLEASED THAT WE HAD NOT CALLED THEM SOONER. I HAVE EXPERIENCED ONLY A FEW AIRBORNE MEDICAL PROBS IN 17 YRS AND NONE OF THEM RESULTED IN DIVERSIONS AND I BELIEVE I WAS THINKING THAT THIS WOULD NOT LIKELY REQUIRE ONE EITHER. THINKING BACK ON IT; HOWEVER; I REALIZE THAT I HAD BEEN GIVEN ENOUGH INFO TO CONCLUDE THAT THE ODDS OF A DIVERSION WERE HIGH ENOUGH THAT I SHOULD HAVE CALLED DISPATCH IN ADVANCE TO LET THEM KNOW OF THE POSSIBILITY.