In a deep, coverable pan, sauté onion and garlic in about 1-2 tbsp of olive oil with a pinch of salt and pepper on medium high heat until onions become translucent.
Add chicken and brown (approximately one minute or so).
Add rice and sauté until rice becomes slightly translucent (another minute or so).
Add chicken broth, water, and about 2 tbsp of red wine vinegar with another pinch of salt and pepper. Mix thoroughly and bring to a boil. Cover tightly, lower heat and let simmer for 15 minutes. Have all the frozen vegetables ready in one container or bowl. Then quickly remove cover add all the frozen vegetables on top of rice, and re cover as fast as you can.
Turn heat off and let sit and steam for an additional 10 minutes.
Add cheddar cheese and stir until the cheese has melted. Salt and pepper to taste and serve.