Pulse mangoes in a food processor until finely chopped.
Bring mangoes, sugar, and water to a boil in a heavy medium saucepan, stirring until sugar is dissolved. Reduce heat and simmer, covered, stirring occasionally, until mangoes are very soft, about 30 minutes. Stir in lime juice and strain thourough a fine-mesh sieve into a bowl, pressing gently on and then discarding solids. Cool, then chill, covered.