1. In a medium saucepan over medium heat, stir in sugar, water, lime, lime zest, and jalapeño.
2. Raise temperature slightly, then allow mixture to come to a low boil.
3. Let syrup boil for 3-4 minutes, then lower heat.
4. Remove the syrup from heat and let cool.
5. Once syrup has cooled, strain and store in a food safe container in the refrigerator. This lime jalapeño simple syrup recipe stays fresh for 2 weeks in the refrigerator.