I usually use flax seed for this super simple mayo base, but ground chia would work as well. The key is using a good blender and adding the oil in super slowly.
2 tbsp ground flax combined with 1/2 cup water
1 tbsp yellow mustard
2 tbsp lemon juice
1 tsp salt
1/2 cup - 1 cup of vegetable based oil (I use canola)
In you blender, combine the flax/water mixture, mustard, lemon juice and salt. With the blender running on high speed, start a SLOW drizzle of oil into the mixture. Keep adding oil until the mayo is thick and glossy, about doubled in size. Store in the fridge.
For a great cocktail sauce, add sriracha.
For tartar sauce, add finely chopped dill pickles along with a small amount of pickle juice.