Hate to bump such an old thread, but it's still cold out in northern regions right now so this is a still a great soup for this weather.
As Johns72604 notes, the soup you are possibly referring to is called Avgolemono
which is Greek Lemon-Rice soup ... however the link in the subsequent post for lamb soup is not the same thing.
You state that the version you had included chicken in it.
To add chicken to the recipes I've included below, you might just add chicken breast that has been cooked through in a pan with butter and cut into dice, etc. to your liking.
Avgolemono's richness and thickness comes from a combination of egg yolks, rice and, depending on your preferences, some thickening agent such as corn starch ... and in some instances cream depending on the recipe you are following.
There are two basic versions of this soup ...and either one might be found at a restaurant.
The first version relies on corn starch as a thickening agent and is a more "everyday" sort of recipe ... this will be a somewhat thicker version and is a bit more "forgiving" to the cook and will withstand temperatures that are a bit more uncontrolled. It will also "hide" better if the eggs scramble a bit from the heat while the soup is being held. It also doesn't require preparation at the line at the time of service ... it can sit in a steam table right along with the other soups.
The second version is typical of a more fine dining sort of restaurant and relies on a classic method of thickening that uses a "liaison" of egg yolks and cream to obtain it's consistency.
In a finer restaurant where the cooking line is more used to producing dishes that require multiple steps, the soup is finished and the egg & cream mixture is added just before service.
AVGOLEMONO (using cornstarch slurry)
add 1/2 cup rice to
7 cups very hot (but not boiling) chicken stock
add 2 L eggs + 2 yolks, beaten
temper the eggs before adding them so they don't scramble ...
Tempering is where you whisk in some of the hot soup to the (bowl of) eggs/egg yolks to bring the temperature of the eggs up gradually before incorporation of the eggs into the bulk of the soup (again while whisking constantly to incorporate).
(See the 2nd recipe below for further info on how to temper.)
juice and zest of 1 very large lemon (add more if needed to taste)
whisk in 2T cornstarch mixed with a little cold milk
Cook until rice is tender and consistency is thickened ... Do not boil.
If preferred, the color of the soup can be enhanced with a very small amount of yellow food coloring.
before serving finish by incorporating
salt to taste
(Note: if thickened sufficiently, the soup is also a really great sauce for use over stuffed grape leaves!)
The second recipe
is the way you would serve it at a restaurant providing that you are set up behind the line to finish the soup when you are ready to sell. This is the preferable method.
AVGOLEMONO (thickened using a liaison)
add 1/2 cup rice to
6 cups chicken stock and cook until rice is completely tender (hold at 180 degrees)
Thoroughly combine 6 egg yolks (from large eggs) and 16oz heavy cream ... gradually add about 1/3 of the stock to the egg/cream mixture, whisking constantly to diffuse the hot liquid.
Then, add the egg/cream/stock mixture back into your main pot of stock, whisking constantly.
Bring and maintain the soup to just below 180 degrees.
(Note that sour cream or creme friache can be used as part or all of the cream component.)
juice and zest of 1 very large lemon (add more of both zest and juice as needed to taste)
salt to taste