Thinly slice the chicken lengthwise so you end up with thin strips, about an inch wide and 5 inches long, depending on the size of the chicken breasts.
If the slices are more than a quarter-inch thick, lay out a piece of clingfilm (saran wrap), lay the slices of chicken on top and cover with another piece of clingfilm. Bash with a rolling pin until each slice is a quarter-inch thick.
Place the chicken in a bowl with the spices, stir and cover. Leave in the fridge for 30 minutes to marinate.
Meanwhile, prepare and preheat the grill.
Using a vegetable peeler, slice the zucchini into thin strips the length of the zucchini.
Thread alternate strips of chicken and zucchini onto the skewers in an "S" shape.
Drizzle with olive oil and grill for about 15 minutes, turning regularly, until the chicken is cooked through.