In 1912-1913 a synagogue was excavated by Andre Plassart on northeast part of the island of Delos. The site was later re–excavated by Philippe Bruneau in 1962. It has been suggested that the synagogue was in use from the Second Century B.C. to the Second Century A.D.
First Maccabees (15:16–23) and Josephus attest to a Jewish presence on Delos at this time.
For example: 1Mac. 15:22 "The consul wrote the same thing [regarding protection of the Jews] to King Demetrius and to Attalus . . . and to the Spartans, and to Delos, and to Myndos, . . . and to Gortyna and Cnidus and Cyprus and Cyrene. 24 They also sent a copy of these things to the high priest Simon."
For a convenient on–line description and bibliography of the synagogue see Gordon Franz "The Synagogue on the Island of Delos and the Epistle of James."