Slice chicken breasts into thinner strips. Generously season with smoked paprika, Italian seasoning, salt, and pepper.
Heat a large, high-sided, heavy-bottomed skillet over medium heat. Add 2 tablespoons of olive oil and the chicken. Cook for about 3 minutes per side. Remove chicken to a plate.
In the same skillet, add orzo, minced garlic, and 1 tablespoon of olive oil. Cook on medium heat, stirring, for about 2 minutes until browned.
Add chicken stock, half of the cherry tomatoes, and ¼ teaspoon of salt. Bring to a boil, then reduce to a simmer and cook for 5-10 minutes, stirring occasionally, until orzo is cooked through.
Add spinach and the remaining cherry tomatoes. Stir on low-medium heat until spinach wilts.
Stir in heavy cream and basil pesto. Season with salt and pepper, if desired.
Return the chicken to the skillet. Allow to simmer in the sauce to heat through and until chicken is completely cooked.