Preheat a grill or griddle pan over medium heat.
In a bowl, whisk together the garlic powder, dried oregano, lemon juice, and olive oil to make the marinade. Season with salt and pepper to taste. Adjust until the marinade tastes well balanced. Set aside half of the marinade to brush on the buns later.
Brush one side of the chicken breast with the marinade and season it with salt and pepper.
Place the marinated side of the chicken on the grill or griddle. Brush the top with more marinade. Grill for about 6 minutes until the underside is nicely marked.
Flip the chicken, brush with more marinade, and cover the grill or pan. Cook for another 6 minutes, or until the internal temperature reaches 165°F (74°C). Remove and let rest for 5 minutes.
Brush the inside of each brioche bun with the reserved marinade. Lightly grill or toast the buns until golden brown, then set aside.
Assemble the sandwich by spreading mayonnaise on the inside of each bun. Layer with butter lettuce, tomato, grilled chicken, Swiss cheese, and red onion.
To make the chia fresca, squeeze fresh lemon juice and set aside. Measure the maple syrup or honey, chia seeds, and a pinch of salt. In a medium pitcher, combine the lemon juice and maple syrup or honey. Stir well. Add the chia seeds and salt, then slowly pour in still water while stirring gently to combine. Pour the chia fresca into glasses and garnish each with a sprig of fresh mint.
Serve the grilled chicken sandwich with carrot sticks and hummus, and chilled chia fresca on the side.