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Beat together sugar, butter and zest. Add eggs, one at time, mixing well. Add lime juice and beat until combined.
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Pour the mixture into a small pan and cook on medium, stirring constantly.
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When it is just about to come to a simmer, and has thickened (will coat the back of your spoon), remove from heat. It will thicken up more as it cools.
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Once it is cool enough to touch, place in a bowl, cover and refrigerate until cold, about an hour.