In a large skillet over high heat, warm the oil. Add chicken, season with salt and pepper. Cook until slightly golden brown and no longer pink on the outside, about 6 - 8 minutes. Transfer to a medium plate.
Turn the heat to medium. Wipe the skillet with a paper towel to remove most of the grease. Melt the butter, and sauté the onions until softened, about 5 minutes. Toss in the button mushrooms. Cook until all the moisture inside the mushrooms has evaporated and they start to get a darker color, about 10 minutes. Season salt and pepper.
Sprinkle the flour over the mushroom and onion. Stir to mix well. Cook for 2 minutes. Turn the heat to medium-low. Pour in the milk slowly in a few turns while stirring. Sauce will thickened Add the bell peppers and continue to cook for 15 minutes.
Add the heavy cream and peas. Cook for 10 more minutes. Adjust seasoning with salt and pepper. If needed, add ½ teaspoon sugar. Serve immediately over rice or pasta.