Found a great Mayonnaise alternative on Yahoo.
Egg-free, Soy-free, Dairy-free Mayonnaise Substitute
meat of 1 avocado, sliced or cut in chunks
juice of one half of a lemon
1-2 heaping teaspoons Dijon mustard (I use the grainy kind)
2 tsp.-1 T milk alternative (rice milk, hemp milk, etc.)
a couple of dashes of paprika
a pinch of salt
a pinch of sugar, if you like your mayo a bit sweeter
I am going to try to make more chicken and salmon salads, but they are just not the same without mayo. Hopefully this alternative bridges the gap.