is it possible to make aioli without using raw egg yolk? I have health problems which make raw eggs a problem. Thanks.

Seabirdskitchen's response reminded of Amanda's recipe on here for a milk mayonaise that contains no egg yolks either:
http://www.food52.com/recipes/3041_milk_mayonnaise_maionese_de_leite

This is a bit tricky to make, but is fantastic. It is the Spanish Allioli - a garlic and oil, no egg mixture with just the right texture.
http://seabirdskitchen.blogspot.com/2008/06/breakfast-outside.html

sorry, kind of in a hurry, but vvv3's advice is rock solid. coddle your egg yolks in a bain marie (stainless steel bowl set in a pot of simmering water), whisking to 140 degrees, at which pasteurization takes place. Remove from heat and proceed with your recipe.

You could also use this method and adapt it to aioli since it is very similar to mayonaise:
http://www.saveur.com/article/Recipes/Mayonnaise

is it a bacterial risk you're concerned about? if so, you can use a coddled egg which is an egg that is simmered until the yolk is slightly thickened, getting the egg to a temperature at which the bacteria will be killed. simmer a room temperature egg for not more than a minute; remove it immediately and rinse under cold water and use immediately.

I remember making aioli or mayo in a cooking class some years ago, using liquid pasteurized eggs. I think these are safer than regular pasteurized eggs if there are health issues.

Can you have pasteurized eggs? I've used them when making aioli before.