Preheat oven to 375 degrees. Lightly season the halibut fillets on both sides with salt and pepper. Cut 4 pieces of parchment paper (12 by 16 inches each) and lay them on a clean work surface. Fold each in half crosswise, making a crease in the middle, then open and lay flat.
Cut yellow squash into julienned strips and divide among parchment rectangles, mounding on one side of the fold. Season with salt and pepper. Lay a piece of halibut on top of each pile of squash. Divide the cherry tomatoes (sliced in half, if large) and olives between the four piles and top each pile with thyme. Drizzle each with oil.
Starting in one corner, fold each packet into a half-moon and seal well. Transfer packets to a rimmed baking sheet, and cook in the oven until parchment puffs up, about 12 to 14 minutes. To serve, place each packet on a plate and cut open with kitchen shears at the table.