Heat a double burner grill pan, griddle pan, or outdoor grill over medium-high heat.
Pour about 1/4 cup extra-virgin olive oil into a shallow dish and add the garlic.
Strip the leaves off a sprig of rosemary and finely chop, about 1 tablespoon. Add the chopped rosemary to the bowl with the garlic and oil. Break the remaining rosemary up into 8 small sprigs about the size of the chicken pieces.
Season the chicken pieces with salt and pepper, to taste, and add them to the garlic mixture. Turn to coat. Wrap the chicken pieces in prosciutto, securing the ham with a sprig of rosemary as you wrap. The sprigs should stick out a bit at the edges of the ham. Drizzle the chicken with more oil and grill for 12 minutes, turning occasionally.
Serve 2 pieces of chicken for each serving, along with some lemon wedges for squeezing over the top. Drizzle with balsamic vinegar and serve.