We investigate the contact electrification occurring when a small water droplet resting on a metal electrode is brought periodically in contact with a hydrophobic film of fluorinated ethylene propylene. It is found that the maximum current increases with the drop volume according to a power law. The time scale for the contact current to develop is consistent with that required for a droplet to spread and is, therefore, longer than the time required to form the electric double layer. Adding salt into the water does reduce the contact current but not entirely, which suggests that any remaining water layer cannot entirely neutralize the charges developed upon contact. With an average power of 0.7 mu W and a peak power near 5 mu W at a frequency of 5 Hz, a 200 mu L droplet of pure water can be used to light up a light-emitting diode.