We have several options for stores on island that you can buy dry, fresh, and frozen organic goods.
If you are coming from off island, you already know the prices are higher for organics, but you should expect to pay a little more than usual, because the organics have to be flown here as refrigerated or frozen cargo.
Payless Supermarket at Micronesian Mall in Dededo has a good selection for non-perishables (soups, grains, etc), toiletries, fresh organic salads, frozen organic prepackaged food, frozen organic vegetables. Occasionally, they carry fresh organic produce such as carrots, apples, oranges, and lemons. Payless is the main grocery store on island with many smaller supermarkets elsewhere. They all carry some amount of organic or vegan options, but the one at Micronesian Mall seems to specialize in healthier foods. You can also request they bring in items at the Micronesian Mall branch.
Of course you will not find everything at Payless, so I usually shop at these smaller but great groceries:
Healthy Hearts in Dededo has unique organic items that you won't find elsewhere. Most of the selection is organic dry goods, weekly fresh organic groceries such as kale, salad, tomatoes, potatoes, squash, apples, etc, toiletries, vitamins. They even have an organic cafe (macrobiotic diet) where you can order fresh juices, sandwiches, meals, fresh organic baked goods etc. You can sign up for their weekly specials or news online. The owners are a local family that are committed to a healthier Guam, and it shows in their store and cafe.
Simply Foods in Agana Heights is run by the SDA church, though they do not preach to the Simply Foods customers. They have a well-run cafeteria/cafe with assorted vegetarian/vegan food with daily specials and fresh wheatgrass. The store in the back has a variety of non-perishables, frozen vegetarian/vegan meals, refrigerated items, toiletries, vitamins. They do not specialize in organics, but do carry organic items. Their grocery prices are pretty reasonable and you can order things in bulk from them with a discount, and request items be brought in. Of course they do not carry meats.
Nuts & Grains is located behind Oka Payless near the hospital and has a small selection of non-perishables and a cafe, but I would not recommend this place, because their non-perishables were not fresh (expired items, which is common for Guam, so check labels before buying!), and the cafe did not serve vegan items. That was a few years ago, so you are welcome to check it out and let me know if things have changed.
Farmer's Markets can be found at Chamorro Village in Agana, Saturday mornings in front of Yigo Payless, everyday in Harmon next to Iglesia Ni Christo Church, once in a while outside of the Barrigada Post Office selling sweet island corn, vegetables, tuba, etc. According to the Department of Agriculture, most farmers on Guam do not use too much in terms of herbicides and pesticides, as compared to farmers in the states who are heavily marketed to. Use a good vegetable wash and find the freshest produce on island!
Any other suggestions for where to shop? Please email me!