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Strymon bebrycia
Thanks to all who helped me ID these guys. Very tiny guys about 3cm, with brown underside of wings and blue hues of the upper wings.
Leaf litter and under blades of grass.
Since the other two suggestions are also so similar I would recommend you to go online to see which species are more often seen in the islands where you spotted the butterfly. It is indeed a hairstreak but pinning the exact species may be trickier.
When I was in Mexico I saw a very similar butterfly:
Red banded hairstreak-Calycopis cecrops
http://www.projectnoah.org/spottings/734...
These are definitely hairstreaks (Family Lycaenidae), but I have been unable to find any information on species that occur in that area.