Seed, core, and finely chop tomatoes. Measure 3 1/2 cups chopped tomatoes; place in a 6- to 8-quart stainless-steel, enamel, or nonstick heavy pot. Bring to boiling, stirring occasionally; reduce heat. Simmer, covered, for 10 minutes. Measure 3 1/3 cups tomatoes; return to pot. Stir in lemon juice and basil.

In a small bowl combine 1/4 cup of the sugar and the pectin; stir into tomato mixture. Bring to a full rolling boil, stirring constantly. Stir in the remaining 2 3/4 cups sugar. Return to a full rolling boil, stirring constantly. Boil hard for 1 minute, stirring constantly. Remove from heat and quickly skim off foam with a metal spoon.

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 for 5 minutes (start timing when water returns to boiling). Remove jars from canner; cool on wire racks. Makes 5 half-pints.