Charlemagne's palace chapel was modeled after the church of San Vitale in Ravenna. The chapel, now the central part of Aachen Cathedral in Germany, was designed as a grand statement of imperial and religious authority.
Construction began around 792 under the architect Odo of Metz, and the chapel was consecrated in 805 by Pope Leo III. Its central octagonal room, surrounding gallery, dome, marble decoration, and mosaics reflect the influence of late Roman and Byzantine architecture. San Vitale, built in sixth-century Ravenna under the emperor Justinian I, provided the most important visual and architectural model.
Charlemagne had visited Ravenna and ordered valuable materials, including marble and mosaics, for his palace complex at Aachen. The Aachen chapel was not an exact copy: its geometry was simplified, and its construction used northern European and Roman building practices rather than reproducing San Vitale's techniques precisely.
A common mix-up is Constantinople, another major source of Byzantine influence. Some scholars identify similarities with buildings there, but San Vitale in Ravenna is the standard answer accepted for this question.