Sprinkle both sides of tuna with salt and pepper.
Heat oil in nonstick skillet over medium-high heat. Add tuna; cook until browned on both sides and just slightly pink in center, about 8 minutes. Transfer tuna to platter.
To same skillet, add chicken broth and lemon juice. Heat to boiling. Remove from heat. Swirl in mustard and chives. Spoon sauce over tuna. Serve immediately.