Preheat oven to 375°F. Line a large baking sheet with parchment paper.
Brush both sides of 2 pita rounds with 1½ tablespoons oil. Cut each round into 8 wedges; place on the prepared baking sheet.
Bake until toasted and crisp, 6 to 8 minutes, flipping halfway through. (Some soft spots are OK; the pita chips will crisp as they cool.) Let cool completely, then break into bite-size pieces.
Combine 6 cups romaine, 1⅔ cups chicken, 1 cup cucumber, 1 cup tomatoes, ½ cup onion, the chopped bell pepper, drained olives, crumbled feta and the pita pieces in a large bowl.
In a small bowl, combine ½ cup hummus, 3 tablespoons lemon juice, ¼ teaspoon cumin, ⅛ teaspoon salt and the remaining 2 tablespoons oil; whisk until smooth.
Drizzle the dressing over the salad; toss to coat.
