Prep all vegetables, chicken, and other ingredients as described in the ingredient list.
Heat the olive oil in a medium skillet over medium heat. Season the diced chicken breast with salt and black pepper. Cook until browned and cooked through, reaching an internal temperature of 165°F (74°C), about 6–8 minutes. Remove from heat and let rest for a few minutes.
Spread the herb mayo evenly over each tortilla. Top with cooked chicken, cucumber, tomato, capers, feta cheese, and lettuce.
Fold in the sides of each tortilla, then roll it up tightly from the bottom to form a secure wrap. Slice each wrap in half.
To prepare the chia fresca: combine lemon juice, water, maple syrup or honey, chia seeds, and salt in a large glass or pitcher. Stir well and let sit for 5 minutes so the chia seeds bloom. Garnish with fresh mint.
Serve the wraps with carrot sticks, hummus, pickle, and chia fresca on the side.