Cut four 13- by 15-inch rectangles of cooking parchment or foil. Fold each rectangle in half crosswise; starting from fold, cut out a half-heart 7 inches wide and 13 inches long. Open each and lay flat. Divide leeks equally among hearts, mounding them on one half of each.
Rinse salmon and pat dry. Place one piece on each mound of leeks. Top equally with chanterelles. Drizzle each stack with 1/2 teaspoon olive oil and 1 tablespoon wine; sprinkle generously with salt and pepper.
Fold bare half of each parchment heart over fish and vegetable stack so that cut edges meet evenly. Fold and pleat packet edges to seal: Starting at top of heart, fold a 1/2-inch section of edge up and in; holding this section down, fold next section up and in, slightly overlapping first to form a pleat. Continue folding and pleating edge until you reach bottom of heart; twist point to secure. Transfer packets to a 14- by 16-inch baking sheet.
Bake in a 400° regular or convection oven until a thermometer inserted through parchment into center of fish reaches 140°, about 10 minutes.
Place each packet on a dinner plate. Open at the table, taking care to avoid steam. Add salt and pepper to taste.
Cleaning mushrooms: Trim off tough or discolored bottoms of mushroom stems and any bruised spots or blemishes. (For shiitakes and oysters, remove the entire fibrous stem.) For firm mushrooms such as portabellas, wipe dirt off with a damp cloth or place in a colander, rinse thoroughly under cool running water, and pat dry with towels. For delicate mushrooms that have lots of places for dirt to hide, such as chanterelles and hedgehogs, submerge in a bowl of cool water and gently agitate with you hands to loose any particles. Drain, rinse carefully under running water, and gently pat dry with a towel.