Melt the butter in a large saucepan over medium heat. Add the onion and cook until it becomes soft, about 4 minutes. Increase heat to medium-high and add broth, thyme sprigs, salt and pepper. Bring to boil and add the orzo. Cook until orzo is tender, about 10 to 12 minutes. Remove from heat and discard the thyme (It's fine and even great if a few of the thyme leaves remain).
Whisk the egg yolks and lemon juice in a bowl until well combined. Whisking constantly, slowly pour the yolk mixture into the hot soup. Stir in the chicken, cover, and let sit for 10 minutes, until the soup has thickened and chicken is warmed through.
Spoon into serving bowls and top with fresh chives.
For a vegetarian option, replace chicken broth with vegetable broth and omit the chicken. Add diced firm tofu and or thinly sliced lemons at the end of cooking.
For Paleo or Keto option, precooked white great northern beans may be used in place of the orzo.