Add stock and lemon juice. Bring to boil, add rice, turn down to low, and simmer until chicken is cooked through (just barely simmer--basically you're poaching the chicken, it should take about 10 to 12 minutes).
Remove chicken, dice.
Beat yogurt and egg together in a medium bowl.
Add 1 cup simmering broth to yogurt, 1/2 cup at a time, whisking constantly (this prevents the yogurt from separating).
Add yogurt mixture to pot, whisking well.
Add salt (adjust to taste).
Return chicken to pan. Over low heat, heat through but do not boil. Serve sprinkled with parsley.