Chemicals work great against varroa, of course. I'd go with chemicals, ideally as a preventative but also if you catch them fast enough.
That said, the bees themselves, if not stressed, also do a pretty good job against varroa. You just have to avoid stacking the deck against what they'd do naturally.
We've had good results replacing solid hive bottoms with mesh. It turns out that bees hate varroa even more than beekeepers and will spot varroa mites on their colleagues and pop them off. If you have mesh bottoms on your hives, the bees walk across the mesh no problem, but the mites fall through the mesh to the ground. With a solid bottom, the mites just climb up from the hive bottom onto the next bee that passes by.
In a natural hive, there would have been no hive bottom for the mite to land on.