Cook rice according to directions in a medium saucepan.
After starting the rice, place carrots, onion, and garlic in a food processor and pulse 3-4 times until chopped.
Add carrots, onion, garlic, and green beans to the rice when there are 15 minutes that remain in rice cooking.
Meanwhile, sautee yellow squash in 1 Tbsp olive oil in a large skillet for about 3 minutes.
Add sugar, salt, and 1 Tbsp soy sauce to the squash, stir for 1-2 minutes.
Add the rice mixture to the skillet and add 1 Tbsp olive oil. Stir and cook for 3-4 minutes.
Add beaten egg and 1 more Tbsp olive oil. Stir and cook until eggs are done (about 4-5 minutes).
Add chicken and 2 Tbsp soy sauce and stir until heated through (about 3-4 minutes).