Preheat the oven to 375°F (190°C).
Slice the zucchinis into thin rounds and mince the garlic.
Cut chicken breasts into even pieces and season with salt, black pepper, and dried oregano.
In a skillet, heat olive oil over medium heat. Add garlic and sauté until fragrant, about 1 minute.
Add chicken pieces and cook until lightly browned but not fully cooked through, about 4-5 minutes.
In a mixing bowl, combine cream cheese with the cooked garlic and chicken, stirring to coat evenly.
In a rectangular casserole dish, layer half of the sliced zucchini evenly on the bottom.
Spread half of the chicken and cream cheese mixture over the zucchini layer.
Repeat layering with the remaining zucchini and chicken mixture.
Top the casserole evenly with shredded mozzarella cheese.
Bake uncovered for 30-35 minutes, or until the chicken is cooked through, zucchini is tender, and cheese is bubbly and golden brown.
Remove from oven and let rest for 5 minutes before serving.