B767-200 at FL390 had the right reverser partially deploy in-flight. An emergency was subsequently declared; the engine secured as a precaution and an uneventful overweight landing ensued.

Narrative

FL390; Mach .814 the Reverser annunciation came on amber over the right N1 display. I was the pilot not flying so I ran the QRH 767 Reverser Unlocked checklist. Since there was no yaw; loss of airspeed or buffet; the checklist ended with operate the engine normally. I elected to contact Maintenance Control via a patch through Dispatch. Maintenance Control advised to look at the engine; I sent the First Officer back to do this. He reported that the reverser sleeve was slightly deployed. Based on this information and advice from Maintenance Control; I decided to land at ZZZ. I declared an emergency and told ATC that we would land at ZZZ. ATC began giving us vectors to ZZZ. Since the sleeve was in fact deployed; I decided to do the rest of the QRH checklist which involved shutting down the engine (single engine time was 12 minutes). The checklist also called for a no-slats/flaps 20 degree landing; and that is how we landed. The landing was of course flat but otherwise uneventful and not overweight. We taxied normally to the gate. Note: as we slowed after landing; the Reverser annunciation went out and on walkaround we found the sleeve fully stowed. After the aircraft was serviced by Maintenance and the Quick Turnaround Chart was complied with; we departed.