Preheat the Oven: Place a rack in the center of your oven and preheat to 425° F.

Assemble the Packets: Tear off 4 squares of parchment that are at least 12 inches on each side. Lay the sheet flat on a work surface. Place equal parts of onions in the center of a sheet, leaving space at the top and bottom.

Add the Fish: On top of the onions, place 1 fish filet so that it runs vertically top to bottom. Lightly sprinkle the fish with salt, pepper, garlic, chives, a few very thin slices of lemon, and drizzle with olive oil. Top with equal amounts of tomatoes.

Fold the Parchment Packets: Lift the right and left sides of the paper up and towards the center, directly above the fish. Touch the two sides together and tightly roll them, folding as you go, until you reach the fish. Now, roll and crimp the top and bottom ends, rolling them towards the counter, away from the center of the fish. When you reach the end, tuck the end underneath the fish. Place the packet on a rimmed baking sheet, using the weight of the fish to hold the ends in place. Repeat with remaining three packets.

Bake the Packets: Place in the oven and bake for 12 to 15 minutes, until the fish is fully cooked through and flakes easily with a fork. Serve warm with a squeeze of lemon juice and basil leaves as desired.