In a large straight-sided skillet, melt butter over medium-high heat. Add shallots and chestnuts. Sprinkle with sugar and cook, stirring until beginning to brown, and the sugar caramelizes in bottom of pan, 3 to 5 minutes.
Add fennel and stock. Bring stock to a boil scraping up any browned bits from the bottom of pan. Add salt and pepper. Reduce to simmer, cover, and cook until fennel is tender when pierced with the tip of a knife, 20 to 30 minutes. Uncover and return to a boil. Cook until liquid is reduced and syrupy, about 5 minutes.
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