Immerse tomatoes in boiling water for about 10 seconds; lift out. Pull off skins and cut out cores and discard. Cut tomatoes in half and squeeze juice into a 2- to 3-quart pan. Chop tomatoes into 1/4-inch pieces; add to pan, along with brown sugar, vinegar, and chilies.
Boil over high heat, stirring often, until tomatoes begin to fall apart and almost all the liquid has evaporated, about 5 minutes. Let cool. Add salt to taste. Serve, or cover and chill up to 2 weeks.