Pat the chicken tenderloins dry and season both sides with salt and freshly ground black pepper.
Heat 1 tablespoon of the olive oil in a large skillet over medium-high heat until shimmering.
Add half of the chicken tenders to the skillet and cook 2–3 minutes per side, until golden brown and cooked through; transfer to a plate and cover loosely with foil.
Add the remaining 1 tablespoon olive oil to the skillet and cook the remaining chicken 2–3 minutes per side until done; transfer to the plate and cover.
Reduce heat to medium and melt 1 tablespoon butter in the now-empty skillet, then add the minced garlic and sauté about 15 seconds until fragrant.
Stir in the tablespoon of flour and cook 1 minute, stirring constantly to form a roux.
Slowly pour in the chicken broth, then add the orange juice and lemon juice while scraping up browned bits from the pan; stir constantly to combine.
Bring the sauce to a simmer and cook about 3 minutes, stirring frequently, until it reduces and slightly thickens.
Remove the pan from the heat and stir in the remaining 2 tablespoons butter, orange zest, and lemon zest until the butter melts and the sauce is glossy.
Return the cooked chicken to the skillet and toss to coat in the citrus sauce; sprinkle with chopped parsley and serve immediately.
