Greek Chicken Kebabs with Tzatziki Sauce

lbs bonless skinless chicken breasts (, diced into 1 1/4-inch cubes)

+ 2 Tbsp olive oil (, divided, plus more for grill)

fresh lemon juice

red wine vinegar

garlic (, minced)

dried oregano

dried basil

dried thyme

ground coriander

Salt and freshly ground black pepper

large red bell peppers (, diced into 1 1/4-inch pieces)

small zucchini ((nearly 1 lb), sliced into rounds slightly under 1/2-inch thick)

large red onion (, diced into 1 1/4-inch wedges)

medium cucumber ((about 8 oz), peeled, seeded and chopped into chunks*)

salt (, plus more to taste)

plain Greek yogurt (1 heaping cups)

garlic (, finely minced)

fresh lemon juice

chopped fresh parsley

chopped fresh dill