First clean the chestnuts with a cloth, cut them crosswise with a small knife with a smooth blade, then cook them for 10 minutes in boiling water together with the thyme.
Leave them in the hot water so that they do not dry out and, being careful not to burn them, take them one at a time and peel them (also removing the inner skin) starting from the incision to make the task easier.
Continue like this with all the chestnuts.
Prepare the syrup by boiling the water with sugar, lemon peel and vanilla (after cutting the pod).
Simmer for 5 minutes, then remove from heat, remove the lemon and vanilla and add the rum.
Arrange the chestnuts in a sterilized jar (here the procedure to do it correctly) and cover them with the still boiling syrup, then plug tightly and let it cool upside down.
The chestnuts in syrup are ready: let them season for 1 month before tasting them.
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