Bring a large pot of water to a boil. Cut a small X in the bottom of each peach; add to the boiling water for 1 minute. Transfer to a bowl of ice water to cool; drain and peel off the skins with a paring knife. (Or for harder peaches, remove skins with a vegetable peeler.)
Chop the peaches. Combine with the sugar, salt and chile in a medium saucepan. Toss and let stand until the sugar dissolves and the liquid is syrupy, 10 to 20 minutes.
Add the syrup to the pan and bring to a rapid simmer over medium-high heat. Reduce the heat and simmer, stirring frequently and skimming off any foam, until the peaches soften and the juices thicken, about 15 minutes. (Gently mash any large peach chunks.) Remove from the heat and let the jam cool to room temperature, stirring occasionally, about 1 hour.
Transfer the jam to a jar or other airtight container and refrigerate until cold and fully jelled, 1 to 2 hours. Store in the refrigerator for up to 2 weeks.