Natural House is a supermarket that touts its organic products. It was established back in 1982 when health foods did not get the attention it does now. There are currently 31 shops, the majority located in the Kanto Region. Their website explains in great detail about their products, the farms and even has an online market. www.naturalhouse.co.jp/ Unfortunately, it is only in Japanese.
I found one store very near Omotesando Station. Natural House – Aoyama I am not a frequent shopper there and thus not confident enough to report on prices, quality, etc. compared to other shops offering similar products. But for those looking for “health” foods, then I hope providing a map for one helps.