Place cardamom, coriander, cumin, fennel, 1 teaspoon salt, and 1/2 teaspoon black pepper into an electric spice grinder or coffee grinder; pulse until finely ground. Reserve 1 teaspoon of spice mixture.
Place remaining spice mixture on a plate. Brush chicken breasts evenly with 1 tablespoon olive oil. Press chicken breasts into spice mixture, coating each side.
To make raita, place grated cucumber on several layers of paper towels, top with additonal paper towels, and pat well to remove excess water. In a bowl, stir together cucumber, yogurt, lemon zest, garlic, cayenne, and reserved teaspoon of spice mixture. Season with salt and pepper. Set aside.
Warm remaining tablespoon of olive oil in a large skillet over medium–high heat. Add chicken breasts, skin side down, and cook in a single layer until skin is golden, about 3 to 5 minutes. Reduce heat to low; turn breasts, season with salt and pepper, and cook until done, approzimately 4–5 additonal minutes.
Place a chicken breast on each plate, add a dollop of raita, and garnish with lemon wedges. Serve immediately.