B777 Captain reported the APU Fire bell and horn sounded and the APU fire handle illuminated after engine shutdown at the gate. No smoke or fire was detected.

Narrative

After taxing into Gate XX and shutting down the engines; the APU FIRE bell and horn went off. The APU fire handle illuminated an alert and the APU fire checklist appeared on the CRT. The APU auto shutdown and the airplane lost power. We accomplished the Fire checklist and fired the APU fire bottle. Since we were at the gate; the flight attendants and passengers began departing the airplane as the door was open and we were busy up front. They noticed the loss of power but continued deplaning.We called maintenance right away to have them come out and I contacted the ground crew person to walk back to the tail and check for any evidence of smoke or fire. They came back and told me they didn't see anything and had no indications on the APU panel on the nose wheel. They then connected ground power. Once we finished all checklists we checked the cabin; all passengers were gone. I walked back to check for any smoke or fire. There was none. I told the 2 FOs they could leave. I sent a write up of the APU fire. I waited for maintenance. After about 10 minutes I called Maintenance Control via Dispatch. They told me this is a chronic condition with this airplane and it has happened several times before. I didn't see it in any of the 10 pages of write ups. They said they will take it to the hanger. They already talked to the local maintenance person in ZZZ and told me thanks. I left the plane and went through customs. Since I can't go outside the plane before clearing customs; I went back to the international terminal and walked by the windows to look at our plane and ensure no fire or smoke. I called the Chief Pilot after talking to Maintenance Control and explained what happened.