Wash, peel, and pit the peaches, then chop them. Layer them with the sugar in a large pot and let them macerate for a few hours or overnight, so they release plenty of juice.
Bring to a boil over medium heat, then simmer, stirring often and skimming any foam, for about 1 to 1½ hours, until thick and glossy. Add the finely chopped lemon zest while it cooks, so it softens and caramelizes into fragrant little bits.
Stir in the lemon juice in the last 10 minutes; it brightens the color and helps the set.
Test the set on a cold plate: drop on a little jam, wait a minute, then push it with your finger. If it wrinkles, it is ready.
Ladle the hot jam into clean, sterilized jars, seal, and let cool. Store sealed jars in a cool, dark place; refrigerate once opened.