Preheat the oven to 375°F (190°C). Place the unbaked 10-inch pie crust in a pie plate and set aside.
Sauté the onion and celery: heat 1 tablespoon olive oil and 1 tablespoon butter in a skillet over medium heat, add the diced onion and celery, and cook until translucent; remove from heat.
Toast the slivered almonds on a baking sheet in the oven for 5–7 minutes, watching closely until lightly golden; set aside.
In a large bowl, combine the sautéed onion, sautéed celery, toasted almonds, diced cooked chicken, lemon juice, mayonnaise, sour cream, condensed cream of chicken soup, drained water chestnuts, herbs, black pepper, smoked paprika, and 3/4 cup of the shredded cheese; mix until evenly combined.
Pour the chicken mixture into the prepared pie crust and spread evenly.
Bake uncovered at 375°F (190°C) for 30 minutes.
Remove the pie from the oven, sprinkle the remaining 3/4 cup shredded cheese evenly over the top, and return to the oven.
Bake an additional 10–15 minutes, until the filling is set in the center and the crust is golden brown.
Let the pie rest 10–15 minutes before slicing and serving.