With a medium-size melon baller, scoop out round balls of the melon. You should have 32 all together. Set aside.
Mix the olive oil, salt, and pepper in a medium mixing bowl. With the goat cheese, form into 1 inch round balls. They can be placed into the olive oil mixture and thoroughly coated.
When preparing the prosciutto, place a slice on a cutting board. Cut down the center, and then roll up so it will fit on the skewer.
Assemble the skewers. Layer the cantaloupe, prosciutto, basil leaves folded in half, goat cheese balls, and the second piece of cantaloupe until you have 16 skewers.
Place on a serving platter. Drizzle the balsamic over the skewers 3 to 4 times. Garnish with more basil.