Greek dressing: combine all the dressing ingredients in a large bowl and whisk to combine. You can also just add them to a jar with a lid and keep the dressing in the jar. Shake thoroughly before using.
Store dressing in a sealed container in the refrigerator for up to a week.
Marinate and grill chicken: add your pieces of chicken to a plastic zip-top bag or sealed container and cover them with half of the Greek dressing that you just made.
Marinate the chicken for 30 minutes or up to 1 hour.
Preheat your grill or grill pan for 10 minutes.
Pull the chicken out of the marinade and cook on grill grates or pan for 4 to 5 minutes per side for thighs and 5 to 6 minutes per side for chicken breasts. If you have very large chicken breasts you might want to grill for 7 minutes. If you have a probe thermometer you should be looking for 165 degrees F (73 C). You should be able to pull the chicken off the grill 5 degrees less than your target temperature and it will carry over those extra degrees.
Allow the chicken to cool and then slice or cut it into bite-sized pieces.
Pita sandwich assembly: open the pita pockets by slicing off the top third of the pita. Save that small piece of pita for a snack.
Toss the lettuce, tomatoes, cucumbers, kalamata olives, feta cheese, and chicken in a large bowl, and then add a few tablespoons of the dressing. Toss the salad again and taste a bit to see if it needs more dressing or salt and pepper. Add those if needed and toss again.
Add a generous portion of salad to each pita pocket, making sure it's stuffed full and almost overflowing. Serve and enjoy.
Notes:
Here's my recipe for simple pita bread.