Whisk together mustard, lemon juice and egg yolk in a bowl.
Add oil to yolk mixture a few drops at a time, whisking constantly, until all oil is incorporated and mixture is emulsified.
Whisk in garlic and chili sauce (or cayenne pepper) to taste. Season with salt. If aïoli is too thick, whisk in 1 or 2 drops of water; it should be creamy, but much looser in consistency than store-bought mayonnaise.