B777 Captain reported oil loss in number one engine and diversion to nearest suitable airport.

Narrative

During cruise at FL360; FO and I noticed slow and steady oil quantity loss on #1 engine. We began logging time per quart loss and determined a very steady rate of 1qt every 25 mins. We also were aware of a large amount of oil being added to #1 engine during preflight servicing in ZZZ3 as entered in ELB (Electronic Logbook). I went on second break at about 3 1/2 hours into flight. At the time oil quantity was at 10 quarts. FO who is very good and did an excellent job; was monitoring oil situation. I instructed them at quantity remaining of 6 qts to initiate a satcom (Satellite Communications) with dispatch/maintenance and get me out of the bunk. Approximately 45 mins into my break; I got a call from FO/Relief Pilot that quantity was indeed continuing to steadily drop; and they had initiated a call to dispatch. I asked them to have [the] Chief Pilot and fleet manager conferenced in on satcom call. I returned to the FD asap and found oil quantity at 7 qts. On the satcom were dispatch who was also great and awesome support; Maintenance Control and [the] Chief Pilot. Shortly after fleet CA joined in the call. We described the situation; but by now oil quantity has continued to drop; down to 5 qts. [The] Relief Pilot calculated based on the steady loss of oil qty; we would reach 0 quantity in about 2 hours. Maintenance Control said they saw a low oil alert on their end; beyond that; they were not much help. We still had almost 6 hours remaining in the flight with a tropical storm and not good weather forecast for most of City X and calculated at the current rate of quantity loss; oil would reach zero approaching second critical point. We were about 2:15 flight time to ZZZ at the time. We made the decision to divert and proceed to ZZZ while everyone was on the satcom call. We requested direct ZZZ from ZZZ2 and was quickly given clearance to ZZZ. No emergency was declared as it was not yet necessary to shut down engine due to no low oil press/high oil temp eicas (Engine Indicating and Crew Alerting System). We proceeded at FL360 to ZZZ; reviewed diversion guide and formulated plan for diversion and possible engine shutdown. We also executed the overweight landing supplementary Checklist due to fact we were projected to be about 10k over max landing weight. Dispatch also volunteered that overweight landing was fine due to minimal inspection. Proceeding to ZZZ oil qty continued to drop; getting to 0 in the terminal environment. We were beginning to get some oil pressure fluctuation on the descent/approach. In flight shutdown was not needed. FO flew approach to Rwy XX and made an absolutely fabulous landing. We landed with 0 indicated oil qty on #1 engine. After taxi to gate and engine shutdown; qty read 4qts. Maintenance met the aircraft on arrival. He opened #1 cowl and after inspection found a chip detector had come out of it it's housing and oil was being siphoned out of the chip detector hole. There was oil all over the interior of the cowling. Crew and I did our best to keep passengers informed of events and I spoke personally and verbally to each cabin once we reached the gate. There were only 3 agents available to assist our passengers at the north terminal (not our regular passenger terminal) and had no computer to use other than their phones but were busting their butts to help everyone. I also verbally debriefed the Chief Pilot after gate arrival. It took quite a bit of time to deplane passengers due to logistics. We finally had everyone off the plane and were able to proceed to hotel at about XA:15 am local ZZZ time.