Sauté onion in olive oil in a medium skillet over medium heat 5 minutes or until tender. Add garlic; cook 1 minute, stirring constantly. Add pineapple juice; cook over medium-high heat until liquid is reduced by half (about 3 minutes).
Combine pineapple and next 3 ingredients in a large bowl; stir in onion mixture. Cover and chill up to 24 hours. Stir in pecans just before serving.
Fix it Faster: Start with a cored fresh pineapple to speed things up when making this salsa.