Place onion, chili, half of cilantro leaves, and salt in a mortar and pestle. Pound into a fine paste. Alternatively, combine onion, chili, half of cilantro, salt, and half of lime juice in a food processor or blender and process until smooth paste is formed, scraping down sides as necessary.
Split each avocado in half, discard pits, and spoon out flesh into a medium bowl. Roughly mash with a stiff whisk. Add onion/chili puree, remaining cilantro leaves, and half of lime juice (if using mortar and pestle method). Fold to combine. Season to taste with more salt and lime juice.