Place the chicken in a bowl and drizzle with the olive oil. Sprinkle the oregano over the top and stir to coat.
Cover the bowl with plastic wrap and refrigerate 6 hours or overnight. About an hour before cooking, remove from the refrigerator and sprinkle the lemon juice over the top.
Let sit about 45 minutes then thread onto skewers. Grill the skewered chicken until cooked through, a few minutes per side.
Brush with a little of the marinade after putting on the grill - but be sure not to put marinade on for the last few minutes so it is cooked through!
Sprinkle with sea salt if desired and serve with homemade tzatziki.