In a 6- to 8-quart heavy pot combine sugar, peaches, and lemon juice. Bring to a full rolling boil, stirring constantly until sugar is dissolved. Quickly stir in pectin. Return to a full rolling boil, stirring constantly. Boil hard 1 minute, stirring constantly. Remove from heat. Quickly skim off foam with a metal spoon. Stir in basil.
Ladle hot jam into hot, sterilized half-pint canning jars, leaving a 1/4-inch headspace. Wipe jar rims; adjust lids and screw bands.
Process filled jars in a boiling-water canner 5 minutes (start timing when water returns to boiling). Remove jars from canner; cool on wire racks.