Heat a large pot of water to a boil. Salt the water and add orzo pasta. Cook to al dente.
Preheat a large nonstick skillet over medium-high heat and add extra-virgin olive oil. Season chicken liberally with salt and pepper and add to the hot skillet. Cook the chicken for 5 to 6 minutes on each side. Remove the chicken from the pan and cover with foil to keep warm.
Return the skillet to the heat, turn heat back a bit, and add the butter. Once the butter melts add the mushrooms and brown stirring occasionally for about 4 to 5 minutes.
Once the mushrooms are brown season with salt and pepper then add the garlic, thyme and shallots. Cook stirring occasionally for about 2 minutes or until the shallots are wilted. Sprinkle the flour into the pan and cook 2 minutes more.
Whisk in the stock, balsamic vinegar and the cream. Turn the heat up to high and simmer for about 2 minutes or until thickened. Slice the chicken on an angle. Add the parsley and the chicken back to the skillet to heat up, about 1 minute.
To serve, pile orzo on dinner plates and top with the sliced chicken and sauce.