Heat the olive oil in a medium skillet over medium heat. Season the diced chicken breast with salt and black pepper. Cook the chicken until nicely browned and the internal temperature reaches 165°F (74°C). Remove from heat and let it rest for a few minutes.
Spread the herb mayo onto each tortilla. Top with cooked chicken, cucumber, tomato, capers, feta cheese, and lettuce.
Fold in the sides of each wrap, then roll it up tightly from the bottom to form a secure wrap. Cut in half.
To prepare the chia fresca, squeeze the lemon juice and set aside. In a medium pitcher, stir together the lemon juice and maple syrup or honey until well combined.
Add the chia seeds and a pinch of salt, then slowly pour in the water while stirring gently to avoid clumping. Garnish with fresh mint.
Serve the wraps with carrot sticks, hummus, pickle spears, and chilled chia fresca on the side.