The Ark of the Covenant is one of the most fascinating of all Temple-related subjects. There are many theories about what happened to the Ark of the Covenant, and speculation abounds as to its actual location. Some people think it was taken to the Vatican, together with other Temple vessels, such as those depicted on the Roman monument, the Arch of Titus. There are many authentic, ancient historical chronicles, and even more popular legends, that attest to many sacred vessels having been taken away to Rome. However, this does not apply to the most holy feature of the First Temple, the Ark.
While some claim to have evidence that the ark is in Ethiopia, and of course, moviegoers were treated to a fanciful version of the story in "Raiders of the Lost Ark," in reality, the expression "lost" ark is not an accurate description for the Jewish people's point of view - because we have always known exactly where it is. So the Ark is "Hidden," and hidden quite well, but it is not lost.
Tradition records that even as King Solomon built the First Temple, he already knew, through Divine inspiration, that eventually it would be destroyed. Thus Solomon, the wisest of all men, oversaw the construction of a vast system of labyrinths, mazes, chambers and corridors underneath the Temple Mount complex. He commanded that a special place be built in the bowels of the earth, where the sacred vessels of the Temple could be hidden in case of approaching danger. Midrashic tradition teaches that King Josiah of Israel, who lived about forty years before the destruction of the First Temple, commanded the Levites to hide the Ark, together with the original menorah and several other items*, in this secret hiding place which Solomon had prepared.
This location is recorded in our sources, and today, there are those who know exactly where this chamber is. And we know that the ark is still there, undisturbed, and waiting for the day when it will be revealed. An attempt was made some few years ago to excavate towards the direction of this chamber. This resulted in widespread Moslem unrest and rioting. They stand a great deal to lose if the Ark is revealed - for it will prove to the whole world that there really was a Holy Temple, and thus, that the Jews really do have a claim to the Temple Mount. (The official position of the Islamic Wakf, the body that governs over the Temple Mount, is that there never was a Holy Temple, and that the Jews have no rights whatsoever to the place).
* such as the staff of Aaron that brought forth almond blossoms during the controversy involving Korach (Numbers 16); the jar of manna that had been placed in the Holy of Holies as a testimony; and the jar of anointing oil.