Preheat oven to 350°.
Heat oil in a large nonstick skillet over medium heat until hot. Add yellow squash, zucchini, onion, and rosemary; cook 20 minutes or until vegetables are tender, stirring occasionally. Cool.
Combine squash mixture, rice, and chives in a large bowl; spoon into a 9-inch pie plate coated with cooking spray. Combine milk and remaining ingredients; stir well with a whisk. Pour over squash mixture. Bake at 350° for 45 minutes or until center is set.