LJ45 CREW HAD LNDG GEAR INDICATION THAT A GEAR DOOR WAS NOT PROPERLY CLOSED.

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AFTER TKOF FROM MDW AND ESTABLISHING A POSITIVE RATE OF CLB; THE CAPT CALLED FOR 'GEAR UP.' I SELECTED THE GEAR UP. WHEN THE GEAR CAME UP; THE WHITE R MAIN INBOARD GEAR DOOR LIGHT REMAINED ILLUMINATED. ALL OTHER GEAR INDICATIONS EXTINGUISHED AS NORMAL. I POINTED THIS OUT TO THE CAPT. HE CONTINUED TO CLB THE AIRPLANE TO OUR ASSIGNED ALT OF 3000 FT AND BEGAN A R TURN TO THE E AS INSTRUCTED BY ATC. THE ENTIRE TIME; HE KEPT THE AIRPLANE BELOW 200 KIAS AIRSPD. (MAX GEAR SPD.) AFTER WE LEVELED OFF AT 3000 FT; HE INSTRUCTED ME TO PUT THE GEAR BACK IN THE DOWN POS. I SELECTED GEAR 'DOWN.' THE GEAR WENT DOWN AND INDICATED 3 GREEN LIGHTS; AND NO WHITE LIGHTS. HE INSTRUCTED ME TO BRING THE GEAR BACK UP. I SELECTED THE GEAR 'UP.' ALL 3 GREEN LIGHTS EXTINGUISHED AS THE GEAR RETRACTED; BUT THE WHITE R MAIN INBOARD GEAR DOOR LIGHT ONCE AGAIN REMAINED ILLUMINATED. (NOTE: BOTH TIMES THE GEAR WAS SELECTED UP; WE GOT THE WHITE LIGHT; BUT NO PHYSICAL INDICATIONS THAT THE GEAR DOOR WAS STILL OPEN SUCH AS RUMBLING OR VIBRATIONS.) ATC INSTRUCTED US TO CLB AND MAINTAIN 13000 FT. AT 13000 FT; THE CAPT INSTRUCTED ME TO TRY CYCLING THE GEAR ONE MORE TIME. I SELECTED THE GEAR 'DOWN.' THE GEAR DOWN AND INDICATED 3 GREEN LIGHTS; AND NO WHITE LIGHTS. HE INSTRUCTED ME TO BRING THE GEAR BACK UP. I SELECTED THE GEAR 'UP.' ALL 3 GREEN LIGHTS EXTINGUISHED AS THE GEAR RETRACTED; AND ALSO THE WHITE LIGHT. ALL INDICATIONS WERE NORMAL; BUT AN AUDIBLE RUMBLE/VIBRATION BEGAN. WE BOTH AGREED THAT SOMETHING WAS NOT RIGHT AND THAT WE PROBABLY HAD A GEAR DOOR OPEN AND EXPOSED TO THE AIRFLOW; EVEN PARTIALLY. THE CAPT INSTRUCTED ME TO CALL OUR MAINT DEPT ON THE AIR PHONE AND ASK THEM FOR THEIR INPUT. HE HANDLED THE AIRPLANE AND RADIOS; WHILE I TALKED WITH OUR MAINT DEPT. MAINT ADVISED US TO NOT USE THE GEAR UNTIL WE NEEDED TO LAND AND FOR USE TO DIVERT TO AN ARPT AND LAND. WE DECIDED TO DIVERT TO IND WHICH HAD MAINT AVAILABLE AND WAS ONLY 25 MINS AWAY WHICH WOULD GIVE US TIME TO BURN FUEL SO THAT WE COULD LAND BELOW OUR MAX CERTIFIED LNDG WT. WE CONTINUED OVER TO IND WITHOUT INCIDENT AND LANDED SAFELY AS THE GEAR EXTENDED NORMALLY. BECAUSE THE GEAR EXTENDED NORMALLY AND GAVE US NORMAL INDICATIONS; AN EMER WAS NEVER DECLARED. AFTER WE LANDED AND TAXIED INTO AN FBO AND PARKED; WE DID INSPECT THE GEAR ASSEMBLY AND FOUND A BENT OUTER GEAR DOOR.