There's a thread on an organic supermarket in Banqiao here.
I'm told there's a completely organic farmer's market here, and they have among other things, organic chicken, organic eggs, some other produce like bananas, and fair trade coffee beans -- and organic salad dressing. I have not been there. They also deliver
, with a delivery fee of NT$100 for orders under NT$1500; they only deliver on Fridays and weekends, and it's best to place your order a few days earlier than that. You'll need at least a little Chinese language ability to arrange deliveries, but not much, and not if you go to the market in person.
248 Farmer's Market Zhongxiao - Friday 14:00-20:00 Saturday 10:00-17:00 台北市忠孝東路四段248巷 Taipei, ZhongXiao E. Rd. Lane 248 7:51 PM
248 Farmer's Market Tianmu - every Sunday 13:00-19:00 台北市士林區基河路258號HOLA和樂家居館 廣場 Taipei,Shilin, Jihe Rd. No.258 HOLA square 7:52 PM