Preheat oven to 200 degrees.
Season both sides of each chicken breast with salt and pepper. Place the flour on a plate and dredge the chicken breasts through it, lightly coating both sides. Set aside.
In a large skillet heat the oil over a medium-high heat. Add the breasts and cook 3 minutes, or until lightly browned. Flip and cook another 2 to 3 minutes, or until cooked through.
Transfer the chicken to an oven-proof plate and place in the oven to keep warm.
Return the empty skillet to the burner. Increase heat to high and add the chicken broth and vodka to deglaze the pan. As the liquid bubbles, scrape the bottom of the skillet with a wooden spoon.
Add half of the lime juice and the jalapenos and cook 30 seconds. Add the tomatoes and bring to a simmer.
In a small glass, mix the cornstarch with the water, then add to the skillet. Cook, stirring constantly, until thickened, about 2 minutes. Remove the skillet from the heat. Stir in remaining lime juice.
Arrange each chicken breast on a plate and top with pan sauce. Garnish with cilantro.