Whisk together chicken stock, lemon juice and capers. Lightly crush the capers.
Season the tilapia fillets with salt and pepper. Then dredge them in flour, shaking off any excess. Set aside.
In a large skillet, melt one teaspoon of butter over medium heat. Turn up the heat to medium-high and brown the butter (it should be a golden brown color). Add the fillets to the pan. Sauté for about 3 minutes on each side (they are done when the fish flakes easily with a fork). Add olive oil to the pan as needed if the pan becomes too dry. Transfer fillets to plates.
Pour the broth mixture into pan, being careful of splatter — it will instantly boil, steam and hiss. Scrape the bottom of the pan to loosen any browned bits. Continue heating and stirring until the mixture is reduced to about 1/2 cup. Remove the pan from the burner and whisk in two teaspoons of butter. Spoon two tablespoons of mixture, give or take, over each fillet.