Pretty strait forward; what if the Chileans had demanded and obtained the cession of the Chincha Islands from Peru, in addition to their other gains, at the end of the War of the Pacific? Chile unquestionably had the capacity to seize the islands and I don't think Peru was in a position to resist as the central government had essentially collapsed by the end of the war.
By the 1880's the guano trade was past its prime but still profitable so it could be an attractive acquisition for Chile.
What say you?
Jack