1If using wood skewers, soak them in water for at least 30 minutes before grilling.
2Cut chicken thighs into roughly 1-inch pieces.
3In a bowl, combine chicken with olive oil, salt, garlic, oregano, black pepper, Dijon mustard, lemon zest and juice. Mix well and refrigerate for at least 30 minutes or up to 24 hours.
4In a food processor, combine flour, yeast, salt, sugar, and olive oil. Pulse 5 times to mix.
5With the food processor running, slowly add warm beer until a shaggy dough forms.
6Turn dough out onto a lightly floured surface and knead for 2 minutes until slightly elastic.
7Cut the dough into 4 equal pieces (about 150g each), shape into balls, cover with a damp paper towel, and let rest for 15 minutes.
8Grate cucumber and squeeze out excess water. In a bowl, combine cucumber, yogurt, mayonnaise, garlic, salt, dill, and lemon juice. Stir until well mixed.
9Lightly flour a surface and roll out each ball of dough to about 8 inches in diameter.
10Preheat grill to 550°F. Grill pita bread for 2 minutes per side.
11Grill chicken skewers for about 12-15 minutes, turning occasionally, until well charred on all sides.
12Remove chicken from skewers and chop into smaller pieces.
13Place chicken in pita, top with tzatziki sauce, tomato-onion relish, and pepperoncini.