Heat the olive oil in a large saucepan or skillet over medium heat. Add the chicken and cook, undisturbed, until the chicken is lightly browned. Transfer the chicken to a plate.
If the pan appears dry, add a little more olive oil. Add the onion and cook, stirring, until fragrant, 2-3 minutes. Stir in the rice, chicken stock, one Tbsp of pesto, lemon zest, lemon juice, and salt.
Add the chicken and any juices from the plate into the rice mixture. Bring to a simmer, then add the tomatoes. Cover and cook until the liquid has absorbed, the rice is tender, and the chicken is cooked through, about 20 minutes.
Spread the remaining Tbsp of pesto over the chicken, then sprinkle with the goat cheese. Plate and serve immediately.