The Chamavi first appear under that name in the 1st century AD Germania of Tacitus as a Germanic tribe that, for most of their history, existed along the north bank of the lower Rhine in the region today called Hamaland after them. Hamaland is the land of the Hamavi. It is in the Overijssel province of the Netherlands. Tacitus (op. cit. 34) locates them to the west of the Frisians.
As these same neighbors became the later Salian Franks, the "consensus" mentioned is the first known agreement among them.
These passages in Tacitus raise the question, if Hamaland is the former territory of the Bructeri, where were the Chamavi before then? One answer is that they occupied the coastal plain to the north (Germans moved almost invariably from north to south). Many settlements are named Hamm, including possibly a modern city, Hamburg. The name may have come from the Germanic equivalent of Chamavi.
The best etymology derives Ham- from common Germanic *haimaz, "home", from Indo-European *tkei-, "settle", from which the High German place-name suffix, -heim. The ham- form, "settlement", seems to have come from Low Saxon-Low Franconian, as we acquired it through Dutch and French. The -avi, an adjectival ending, later resulted in -au in other place names, but was dropped in this one. Chamavi in this derivation would mean "men of the settlements" or "settlers." When and in what sense they were so is lost in prehistory.
Ptolemy gives us the answer indirectly. In Geography (2.10), he tells us that the Kamauoi (Latinized to Camavi) were next to the Chaerusci, who in Tacitus are in Lower Saxony near Hanover, or perhaps Thuringia and Anhalt. Apparently, some Chamavi abandoned their lands to move upriver. The reasons are not known. The Romans retained military control of those lands, but the Germanics claimed a right over them.
Two other peoples of Ptolemy wear the *haimaz name: the Chaemae and the Banochaemae. These polities were in what became the High German range. There is no reason to assume they were the Chamavi, although the identification cannot be ruled out either. Ptolemy treats them as distinct peoples.
The name of the Franks was assigned to the Salians right from their first debut on the stage of history. The Panegyrici Latini, a series of twelve speeches given in praise of Roman emperors, describe the efforts of Constantius Chlorus, father of Constantine the Great, to pacify the Franks, who are kept distinct from the Chamavi. These Panegyrici are often attributed to Eumenius, magister memoriae (private secretary) to Constantius, resulting in the compromise name of pseudo-Eumenius.
Some Romans at least did consider the Chamavi to be Franks. On the Peutinger map, which dates to as early as the 4th century, is a brief note written in the space north of the Rhine,
The Chamavi also appear in the 5th century Notitia Dignitatum as a Roman military unit. Long before then, however, we hear of them in a letter of Flavius Claudius Julianus (Julian the Apostate, because he reverted from Christianity to paganism) to the Athenians. He says that he forced the Salii to sue for peace and drove the Chamavi out of Gaul.
The full story is told in Ammianus Marcellinus (17.8-9). The two tribes knew they were where they were not supposed to be, but apparently were hoping not to have to fight. When Julian approached with a business-like force, they sent envoys begging for peace in exchange for returning home and promising to stay there. Julian dismissed them with assurances but with no definite answer and then secretly trailed the envoys to the locations of their armies, which he attacked with the element of surprise. Some of the Chamavi were killed, others put in chains, and the rest fled to their homes, to send envoys later petitioning Julian from a supine position. This time peace was accepted. The Chamavi were to make payments of grain, but none were probably ever made, due to further Roman troubles.