Pat the chicken breasts dry with paper towels. Season both sides with kosher salt and black pepper.
Heat olive oil in a large skillet over medium-high heat until shimmering.
Add the chicken breasts to the skillet and cook for 5-6 minutes on each side, or until golden brown and cooked through (internal temperature reaches 165°F). Remove chicken from the skillet and set aside on a plate.
Reduce heat to medium. Add the minced garlic to the skillet and sauté for 30 seconds until fragrant, stirring constantly to avoid burning.
Pour in the chicken broth, fresh lemon juice, lemon zest, and dried oregano. Stir to combine and bring the mixture to a simmer.
Allow the sauce to simmer for 3-4 minutes, reducing slightly.
Add the fresh baby spinach to the skillet and cook, stirring frequently, until the spinach is wilted, about 2 minutes.
Return the cooked chicken breasts to the skillet, spoon some sauce and spinach over the top, and cook for an additional 1-2 minutes to heat through.
Remove from heat and serve immediately, spooning extra lemon sauce and spinach over the chicken.