Combine sliced peaches, brown sugar, and vinegar in a stainless steel stockpot. Cook over medium heat, stirring occasionally, until peaches are tender but still retain their shape. Set aside.
Combine apples and remaining ingredients in a large stainless steel stockpot. Cook over low heat, stirring constantly, until thoroughly blended. Stir in reserved peach mixture; cook over medium heat, stirring frequently, 5 minutes or until thoroughly heated.
Quickly ladle chutney into hot sterilized jars, leaving 1/2-inch head space. Remove air bubbles. Cover at once with metal lids, and screw bands tight. Process in boiling-water bath 15 minutes.