Homemade mayonnaise is super easy to make at home with just a few simple ingredients, which makes your favorite chicken salad both better tasting and free of any weird additives found in commercial mayonnaise.

Homemade Mayonnaise
makes about 1 cup
1 raw or pasteurized egg (see below)
1 tsp Dijon mustard
1 c grapeseed or safflower oil
1 Tbsp lemon juice or white wine vinegar
salt and white pepper to taste

Place the egg and mustard in a blender or food processor. With the machine running, slowly add the oil in a steady stream. As you do this, you will see the egg and oil begin to thicken. Add the lemon juice/vinegar, and the salt and pepper. Store in the refrigerator and use within a week.

I typically use raw eggs for my mayonnaise, as the risk of salmonella contamination in raw eggs in the U.S. is pretty low (about 1 in 20,000, according to the CDC). Nevertheless, populations with compromised immune systems (such as those taking immunosuppresants for diseases like Ulcerative Colitis and Crohns) may choose to be more careful. In that case, you can use pasteurized eggs, which will lower your risk even further. In his book, On Food and Cooking (which devotes a dense 50 pages to everything you ever wanted to know about eggs), Harold McGee recommends holding eggs at a temperature of 140 degrees for 5 minutes in order to kill any bacteria present inside or outside the egg. You can sometimes find pasteurized eggs in the store, or, with a thermometer and some time on your hands, you can attempt to pasteurize eggs at home like this:

Fill a pan of water with the eggs to be pasteurized and cover with water by at least one inch. Attach a candy thermometer to the pan to track the temperature. Over low heat, slowly raise the temperature of the water to 140 degrees. The goal is to heat the water slowly so that the internal temperature of the eggs is the same as the temperature of the water. Heating too quickly will lead to hot water but cold eggs. Once the temperature of the water hits 141 degrees, set your timer for 5 minutes. During this 5 minutes, adjust the temperature of your stove as needed in order to keep the temperature of the water between 141 and 149 degrees (above 150 or so, the eggs will start to curdle). Once the time is up, remove the eggs and use immediately or store in the refrigerator. These can now be used in any recipe calling for raw eggs, such as mayonnaise, hollandaise, custards, etc. A quick disclaimer: this is my best attempt at pasteurizing eggs for raw use. I cannot  guarantee with 100% certainty that this will eliminate all bacteria from your eggs. If you are truly concerned, my suggestion would be to skip foods with raw eggs and always cook egg dishes to 165 degrees and above.