Place the vinegar in a small saucepan and bring just to a boil. Turn off the heat.
Place the basil leaves in a clean jar and pour the warm vinegar over them.
Place a lid on the jar and let it sit in a pantry or dark shelf for about two weeks.
Taste, when the flavor is to your liking, strain into a lidded bottle.
Video
Notes
Vinegar - use white wine, rice vinegar or even apple cider vinegar. I have even been known to use just plain old white distilled vinegar when that was all I had. This will keep almost indefinitely, but I do make a fresh batch or two every summer.