I think it is always a good idea to try all normal avenues before simply adding chemicals to kill the algae. Keep your water pristine, and look into a way to grow the algae in a small external container (in the DIY section there is a "Nitrate Remover" setup that, as far as I've seen, will always clean up your algae). If you have reasonable amounts of light, clean water and you clean your tank regularly, you shouldn't have any problems.
Algae isn't a big problem, anyhow, unless it is directly affecting the filtration or something similar. It can't survive without eating Nitrates out of the water (which might be why it is reading at 0 right now), and try to take it easy. Algae doesn't harm your fish, and it is a minor nuisance (comparatively speaking).
Hope all goes well, and keep us updated.