Heat saute pan over medium heat. Add 1 tablespoon of olive oil to pan. When hot, add chicken and cook until juices run clear, about 3-4 minutes. Remove from pan and set aside.
Add remaining tablespoon of olive oil. Add onions and mushrooms to pan and cook until onions are translucent and mushrooms have browned (about 4-5 minutes). Add garlic and cook for another 30 seconds.
Add chicken broth to pan, scraping the bottom of the pan to deglaze. Then, add orzo, parsley, and thyme. Stir to combine. Bring to a boil, cover, and reduce heat to low. Simmer until pasta is just al dente (according to your pasta's package directions). Most of the liquid should be absorbed.
Remove lid and add heavy cream and cooked chicken. Stir to combine. Cook for one additional minute, then remove from heat. Allow to set for 5 minutes to allow sauce to thicken.
Optionally, top with fresh chopped parsley, or freshly grated parmesan.