Add lemon juice, oregano, oil, chicken breast, zucchini, and fennel to a resealable plastic bag. Let chill for at least 20 minutes. Take chicken out of bag and throw away marinade.
Steam garlic in boiling water for 3 minutes. Strain and cool.
Skewer 4 chicken strips, 3 zucchini slices, 2 fennel wedges, and 2 garlic cloves, alternately onto each of 6 skewers. Season with salt and pepper. Lay kabobs on cooking spray coated grill rack and cook 4 minutes per side.