In a process for making a multi-chambered container that is lightweight, relatively inexpensive to produce, and that requires less external reinforcement against flexure than conventional multi-chambered containers do, a parison is heated and inflated to form the container. Further, first and second pinched-in areas are fashioned in the sidewall of the container. The first pinched-in area includes first and second wall portions that extend inwardly toward an interior of the main body of the container, and a first end wall portion connecting the first and second wall portions. The second pinched-in area includes third and fourth wall portions that extend inwardly toward an interior of the main body, and a second end wall portion connecting the third and fourth wall portions. The first end wall portion is joined to said second end wall portion so as to define separate compartments within said main body, and wherein the first end wall portion is laterally offset from the second end wall portion, whereby the flexibility of the main body about the joint of the first and second wall portions is minimized. In the next step, the container is cooled.