Season the chicken with 1/2 teaspoon salt and 1/4 teaspoon pepper. Heat the oil in a large skillet over medium-high heat. Working in 2 batches, cook the chicken until browned and cooked through, 2 to 3 minutes per side; transfer to plates.
Add the tomatoes to the skillet and cook over medium-high heat, stirring occasionally, until they begin to burst, 2 to 3 minutes.
Add the wine and simmer until the liquid is reduced by half, 2 to 3 minutes. Stir in the scallions and tarragon and serve with the chicken.