Place the black beans, mango, crab meat, cherry tomatoes, green onions, and cilantro in a large bowl. Toss to combine.
Zest one lime over the salsa, then juice and add the juice to the salsa. Juice a second lime and add to the salsa.
Add the extra virgin olive oil, salt, and pepper to the salsa. Toss to combine and serve immediately with tortilla chips. Store in the fridge in a tightly sealed container for up to three days.