Peel 5 of the oranges. Using an electric centrifugal juicer, juice the peeled oranges. Cut one orange into quarters and juice all of it, including the skin. The juicer should help produce a foamy, whipped texture. Alternatively, use 2 cups fresh squeezed orange juice (from about 6 navel oranges). Slice the remaining orange.
Fill 6 Collins glasses with ice and evenly divide the Campari among them. Top each glass with the freshly squeezed orange juice and an orange slice.