Pat the chicken breasts dry with paper towels. Season both sides evenly with salt, black pepper, and paprika.
Heat the olive oil in a large skillet over medium-high heat until shimmering.
Add the chicken breasts to the skillet and cook for 5 to 6 minutes on each side, or until golden brown and cooked through (internal temperature of 165°F). Remove the chicken from the skillet and set aside on a plate.
Reduce the heat to medium and add the butter to the same skillet. Once melted, add the minced garlic and sauté for about 1 minute until fragrant, stirring constantly to avoid burning.
Pour in the chicken broth, lemon juice, and add the lemon zest. Stir to combine and bring the sauce to a simmer.
Add the fresh spinach to the skillet and cook, stirring occasionally, until wilted, about 2 to 3 minutes.
Return the cooked chicken breasts to the skillet, spoon some sauce and spinach over the top, and cook for an additional 2 minutes to reheat the chicken and meld the flavors.
If desired, sprinkle crushed red pepper flakes over the dish for a mild heat.
Serve the skillet lemon chicken topped with the spinach and lemon-garlic sauce immediately.