Prepare a charcoal or gas grill for medium-high heat (you can hold your hand at grill level only 3 to 4 seconds).
In a medium pot, bring chicken broth and 2 cups water to a boil. Add orzo and cook until tender to the bite, about 8 minutes. In a medium bowl, mix 1 tbsp. olive oil, lemon zest, lemon juice, chives, and 1/4 tsp. salt. Drain orzo and transfer to bowl; toss with lemon mixture. Cover and set aside until ready to serve.
Meanwhile, in a large bowl, combine 2 tbsp. olive oil, ouzo, rosemary, 1/2 tsp. salt, and pepper. Add shrimp and toss. Set aside for 15 minutes.
Trim ends off zucchini and cut on the bias into long, oval, 1/4-in.-thick slices. Brush slices with remaining 1 tbsp. olive oil and sprinkle with remaining 1/4 tsp. salt. Set aside.
Drain shrimp, reserving marinade, and thread onto skewers.
Grill zucchini slices and shrimp skewers, covered, 3 minutes. Turn slices and skewers over, brush shrimp with reserved marinade, cover, and cook until zucchini is soft and browned and shrimp is pink and starting to brown, about 3 minutes. Transfer to a platter and serve immediately, with lemon orzo on the side.
Note: Nutritional analysis is per serving.