DIVERSION TO ANOTHER ARPT FOR LNDG WHEN A B737-300 FLT LOSES ITS MAIN 'A' HYDRAULIC SYS S OF IND; LNDG AT MDW; IL.

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FL350; WHILE ENRTE TO IND; THE 'A' SYS ENG DRIVEN HYD PUMP LOW PRESSURE LIGHT ILLUMINATED; FOLLOWED BY LOSS OF 'A' SYS HYD QUANTITY. QRH ITEMS FOR LOSS OF 'A' SYS HYD QUANTITY WERE COMPLIED WITH. DISPATCH WAS NOTIFIED OF THE HYD SYS LOSS; AND THE WX WAS CHKED FOR IND AND MDW. THE OPC WAS CHKED FOR ADEQUATE RWY AVAILABILITY AT IND AND MDW. MAINT CTL WAS CONSULTED REGARDING THE LOSS OF THE 'A' HYD SYS. WE 3 CONCLUDED THAT I COULD SAFELY DIVERT TO MDW. I MADE THE DECISION TO DIVERT TO MDW WITH DISPATCH'S CONCURRENCE. ATC WAS NOTIFIED. FLT ATTENDANT A WAS BRIEFED ABOUT THE LOSS OF THE HYD SYS AND MY DECISION TO DIVERT. I INSTRUCTED HER TO BRIEF FLT ATTENDANTS B AND C AND ASKED THAT THEY REASSURE THE PAX THAT THERE WAS NO NEED FOR ALARM. I BRIEFED THE PAX AND TOLD THEM OF MY DECISION TO DIVERT TO MDW. SPECIAL CONDITIONS AND HANDLING REQUIREMENTS WERE DISCUSSED WITH THE FO. MDW OPS WAS NOTIFIED; REQUESTING THAT A TUG MEET US AT THE END OF TXWY 4R. WE HAD NO ALTERNATE NOSE WHEEL STEERING SWITCH IN THIS ACFT. MDW APCH VECTORED FLT FOR A LONG FINAL TO RWY 4R. THE LNDG WAS UNEVENTFUL. THE ACFT WAS SHUT DOWN ON THE RWY. MAINT PINNED THE GEAR; AND THE ACFT WAS TOWED TO THE GATE. SUPPLEMENTAL INFO FROM ACN 581038: WHEN CLOSE; (100 NM); ATC ASKED FOR US TO ALLOW INCOMING ACFT TO LAND FIRST. WE ENTERED HOLDING AND EVENTUALLY WERE SLOWED DOWN; VECTORED FOR A 15 NM FINAL. NO SPECIAL HANDLING FROM ATC; NO EMER DECLARED. WE DID NOTIFY MDW TWR; THROUGH ATC; THAT WE WOULD HAVE TO STOP ON THE RWY AND BE TOWED OFF. THAT TOOK 5 MINS.