Peel and seed papaya; cut into 1/2-inch cubes.
In a bowl, mix papaya, onion, chili, cilantro, and lime juice. Add salt to taste. Set aside while preparing fish or cover and chill up to 4 hours.
Rinse fish and pat dry. Coat both sides of steaks with oil and sprinkle all over with salt and pepper. Heat a 10- to 12-inch nonstick frying pan over high heat; add fish and cook, turning once, until opaque on both sides but still pink in the center (cut to test), 4 to 6 minutes total. Transfer steaks to plates and spoon salsa over servings.
*Look for troll- or pole-caught Pacific albacore tuna; it's more sustainably fished than longline, and the fish have lower mercury levels. U.S. ahi is next best.