Bring 3 cups chicken broth to a boil in a saucepan.
While the stock is coming to a boil; heat a large nonstick skillet over med-high heat with the olive oil.
Season the chicken with salt, pepper, and red pepper flakes; add chicken to the hot skillet and cook 3-4 minutes or until the chicken is lightly browned.
Scoot the chicken over to the edges of the skillet, then add in the onions and garlic; continuing to cook for 3 more minutes.
Add the remaining cup of chicken broth and cook 3-4 minutes or until reduced by half.
While the sauce is reducing, whisk the quick-cooking polenta into the boiling broth in the saucepan until it masses; stir in the mascarpone cheese and Parmigiano and season with salt and pepper; you want the polenta to be slightly loose; if it gets too tight, stir in some more broth to loosen it up a little.
To finish the chicken, add in the yellow and red grape tomatoes, stir to combine and continue to cook for 1-2 minutes or until the tomatoes are heated through and starting to burst.
Add in the basil and toss with the chicken and tomatoes.
Serve the polenta in shallow bowls and top with the fresh tomato and basil chicken.