Stir together 1 teaspoon of olive oil, 2 tablespoons of balsamic vinegar and 1 clove of minced garlic in a bowl. Add the chicken to the bowl, turning to coat. Cover the bowl with plastic wrap and let the chicken marinate in the fridge for about 30 minutes.
Boil a large pot of water and cook pasta according to package instructions.
Put the garlic and olives in a food processor and pulse until it becomes a very finely-chopped, pesto-like paste.
Heat the 1 teaspoon of olive oil over medium in heat a skillet. When the oil starts to shimmer, transfer the olive and garlic mixture to the pan and cook it for a minute or so, until the garlic turns fragrant.
Scrape the olive mixture out of the skillet and set it aside. Return the skillet to the heat, crank the heat up to medium-high and cook the chicken about 4 minutes per side until it's nicely browned and no longer pink in the middle. You'll know the chicken is done when a thermometer registers an internal temperature of 165 °F.
Set the chicken aside to rest for about 5 minutes before cutting into bite-size pieces.
Drain the pasta and combine it with the olive mixture (you might need to use a little bit of extra water leftover from boiling the pasta to loosen up the sauce.) Arrange the chicken on top.