As you suspect, the noise probably has less to do with foraging, as the familiar fat-cheeked eastern chipmunk (Tamias stratus) can easily collect and store a life-time supply of food in a single season, than with protecting territory and warning off interlopers.
Chipmunks have a variety of vocal sounds, not all of them translated by scientists, but the one you describe, which has also been rendered “chip-chip-chip” or “chuck-chuck-chuck” or “chipp-R-R-R,” is often associated with driving away an intruder perceived as threatening the burrow.
The high-pitched sound is repeated every few seconds and may be echoed by a chorus of concerned neighbors.
The scolding is probably being delivered by females, as they are apparently even more territorial than the males.
But neither sex is particularly gregarious, except for the period around mating, when the couple may play and vocalize together for some time. Shortly afterward, the male is vociferously driven off.
The female can have two litters a year, and the young are, in turn, loudly urged to leave home in six to eight weeks.