The claim is that Menelik, the son of Solomon and Sheba, took the Ark to Ethiopia. It’s fairly well documented that Jews have been there for about 3,000 years, and that their traditions and practices are ancient, evolving very little over the milleniums.
When Italy first invated Ethiopia in 1898, they were soundly defeated, and it’s said that the vastly-outnumbered Ethiopians carried the Ark in battle.
I saw a great documentary on PBS a year or two ago. The Archbishop of Canterbury happened to be in Ethiopia when it was being filmed, and was asked his opinion. I found it quite telling in the way he accepted the possibility that the Ethiopian Church might actually have the Ark. He could just have easily offered a “no comment,” but he went out on a limb in accepting the possibility, and in refusing to offer any doubt.
It’s also worth noting that the Ethiopian Orthodox Church has never insisted that they have the Ark, nor have they tried to prove that what they have is the Ark. They leave it up to the individual to believe or not believe. Some might see this as a sign that they know they don’t really have it; others might see it as a sign of supreme confidence.
A concise but informative article can be found at:
cwo.com/~lucumi/ethiopia3.html