Heat the oven: Preheat the oven to 375°F. Grease a 2-quart baking dish and set it aside.
Toast the almonds: In a dry skillet over low heat, toast the almonds just until fragrant and golden brown, stirring frequently. Keep a close eye on them, because the nuts can burn quickly. Transfer to a plate.
Soften the vegetables: In the same skillet, heat the olive oil over medium heat. When the oil shimmers, add the celery and onion. Cook, stirring frequently, until the onion is translucent, about 5 to 7 minutes. Stir in the garlic and cook until fragrant, about 30 seconds.
Season the chicken: In a large bowl, stir together the almonds, celery, onion, garlic, chicken, salt, and pepper.
Mix the creamy sauce: In a medium bowl, stir together ½ cup of the cheddar cheese, mayonnaise, sour cream, lemon juice, and chives.
Combine and taste: Add the mayonnaise mixture to the chicken mixture and stir until everything is coated. Taste, then season with additional salt and pepper as needed.
Fill and top the dish: Transfer the mixture to the prepared baking dish. Sprinkle with the remaining ½ cup of cheddar cheese, then scatter the crushed potato chips over the top.
Bake uncovered: Bake until the cheese melts and the filling is hot and bubbly at the edges, about 20 to 25 minutes.
Garnish and serve: Finish with fresh parsley or sliced green onions and serve warm.