Squeeze limes to get 1 cup fresh lime juice, set aside. You can make this job easier with an Electric Citrus Juicer
Make simple syrup by combining sugar and water in a heavy bottom sauce pan and bringing it to a boil. Stir until water is clear. remove from heat, and set aside to let cool.
In a blender combine frozen pineapple, pineapple juice, and lime juice, and blend until smooth.
Fill pitcher with pineapple lime mix and simple syrup, and ice, chiffon (cut into strips) basil, and stir it all together.