Preheat the oven to 180°C. Put the chicken breasts in a medium-sized cooking pan, cover with boiled water and cook with the lid closed in about 10 minutes until tender. Drain. Pull the chicken apart into thin strips with two forks. Heat some olive oil in a large skillet and fry the chayote until soft in about 10 minutes.
Spread the tortillas over a baking sheet and coat with some olive oil. Pierce the tortillas a few times with a fork. Bake in the oven until golden brown and crispy for about 5 to 10 minutes.
Heat olive oil in a second skillet and fry the pulled chicken a few minutes until golden brown. Season with the Mexican herbs, pepper and salt.
Mix the mango with the onion and lime juice. Mix the chayotes with the lime zest and season with salt and pepper.
Top the crunchy tostadas with chayote, pulled chicken and mango salsa.