Combine potatoes, salt, and chives together in a bowl.
Place 1/4 of potato mixture on each of the fish filets, packing mixture onto fish tightly and fully.
Heat oven to 350 degrees.
Heat olive oil in a large, oven proof skillet over medium high heat. Cast iron would be ideal.
When oil begins to shimmer, place fish filet, potato side down, into the skillet. Continue to cook potato side down until hash browns become golden brown. Place skillet in oven and continue to cook until fish is cooked though, about 12 minutes.