Heat oil in a 2-qt. saucepan over medium heat to 350°. Using tongs, submerge 1 chile into oil, and cook 5 seconds; remove and drain on paper towels. Let cool 5 minutes or until completely cool. Repeat with remaining 2 chiles. Remove and discard stems. Process remaining portion of chiles in food processor 30 seconds to 1 minute or until crumbled into small flakes.
Cook garlic in hot oil in same saucepan over medium heat, stirring occasionally, 3 to 4 minutes or until golden. Let stand 5 minutes.
Stir in chile flakes, lime juice, and salt. Store in an airtight container in refrigerator up to 5 days. Allow mixture to come to room temperature before using.
*2 Tbsp. sweet paprika may be substituted. Omit Step 1; proceed with recipe as directed, stirring in paprika with lime juice and salt in Step