In a food processor, whirl egg, garlic, chile, 1/4 tsp. salt, and 1 tbsp. lemon juice until mixture thickens slightly, about 1 minute.
Add oil drop by drop through top of processor until mixture starts to get quite thick, then drizzle in the rest in a slow stream. Whirl in more salt and lemon juice to taste. Mayonnaise keeps, covered and refrigerated, 1 day.