Combine the salt and water in a 4-quart container and stir until the salt has dissolved, 1 to 2 minutes. Add the salmon filets, making sure they are fully submerged. Cover and refrigerate for 3 hours.
Remove the salmon from the brine, rinse thoroughly, and pat dry. Place the salmon, skin-side down, onto a wire cooling rack set in a half-sheet pan. Dry in the refrigerator until the skin becomes shiny and somewhat tacky to the touch, 21 to 24 hours.
The next day, turn the smoker filled with the unsoaked chips on so that it maintains a temperature of 150 to 160ºF. Place the salmon on smoking racks, skin-side down, separating them by at least 1/4 inch and place into the smoker. Adjust heat as needed and cook until the fish is cooked through, has darkened in color, and has the desired level of smoke flavor, 2 1/2 to 3 hours.
Refrigerate unused portions in an airtight container for up to 1 week, or vacuum-seal and refrigerate for up to 1 month.