Seed and peel mangoes. Place mangoes in a large bowl. Use a potato masher to crush mangoes into a smooth pulp. Measure 4 cups mango pulp.
In a 6- to 8-quart heavy pot combine mango pulp, lime juice, and chile peppers. Stir in sugar. Bring to boiling over medium heat, stirring to dissolve sugar. Quickly stir in pectin. Bring to a full rolling boil, stirring constantly. Boil hard 1 minute, stirring constantly. Remove from heat. 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 10 minutes (start timing when water returns to boiling). Remove jars from canner; cool on wire racks.