Preheat oven to 350°F. Grease a 9 x 13-inch baking dish; set aside.
In a medium skillet, heat olive oil over medium-high heat. Add the onion and celery to the skillet and cook, stirring frequently, until the vegetables start to soften, about 5-7 minutes. Remove from the heat and transfer to a large bowl.
Add the chicken, cooked wild rice, thawed broccoli, condensed soup, chicken broth, sour cream, and mayonnaise to the large bowl with the onion and celery. Stir to combine. Transfer the chicken mixture to the prepared baking dish.
Sprinkle grated cheese over top.
In a separate bowl, stir together Ritz cracker crumbs and melted butter. Sprinkle on top of the casserole.
Bake, uncovered, for about 25 minutes (or until hot, bubbly, and golden brown on top).