For the chicken, combine all of the ingredients in a large bowl (except for the chicken) until well combined. Add the chicken and mix until fully incorporated with the marinade. Cover tightly with plastic wrap and allow to chill for at least 1 hour, or overnight.
For the aioli, whisk all of the ingredients in a medium bowl until smooth and somewhat thick. Cover with plastic wrap and chill until ready to use.
For the fries, peel and cut the potatoes into thin long slices. Submerge in water to keep from browning.
Heat the oil in a large pot until 325 degrees F. Fry the potatoes in batches, making sure to dry them well before putting in the oil. Fry for about 3 minutes until soft but not browned. Transfer to a wire rack, set over a baking sheet and continue frying the rest.
Raise the temperature of the oil to 375 degrees F. Refry the potatoes in batches, for about 4 minutes until golden brown and crispy. Transfer to wire rack and continue frying the rest. Season with salt as soon as they come out of the oil. Keep the fries warm in a preheated 250 degree F oven.
Cook the chicken in a skillet or stove top grill for about 4 to 5 minutes on the first side. Flip over and continue to cook for about 2 to 3 minutes. Transfer to a plate or platter and allow to rest for about 10 to 15 minutes before cutting. You might have to cook the chicken in batches, depending on how big your skillet or grill is.
Once you're ready to assemble, pile the fries onto one large platter or 4 individual plates and drizzle with the garlic aioli and hummus. Top with the chicken and your desired toppings, finishing off with a bit of dried oregano at the end. Eat immediately. Enjoy!