Looks like Cuban serpentine, also known as Verde Serrano.
Serpentine is a green metamorphic rock/marble that is most commonly found in regions of subduction faulting (California Sierras and Italy also have beautiful green serpentines). Some of that white "webbing" in the green is a form of asbestos, iron is also present (giving it is distinctive color). No need to worry about the asbestos content unless you choose to smash this beautiful bird into pieces, releasing asbestos particulates into the air. As is, it is very safe.
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“Let’s work the problem, people. Let's not make things worse by guessing.” -Gene Kranz, Mission Control Director (played by Ed Harris), Apollo 13
