The place pictured is now closed (made way for some more development), though of course there are many very similar places around Chiang Mai, serving Buddhist-Vegan food.
Vegetarians who visit Thailand on holiday seem to be either raving about the veggie food, or seriously struggling to find something. For some reason there doesn't seem to be a lot of middle ground. The ravers are correct of course, Thai vegetarian food is excellent and very varied. Yet for some reason it takes people a while to recognize the vegetarian places and to get the hang of ordering dishes 'sans-meat' at regular restaurants and food-stalls.
Most Thai vegetarian food is actually Buddhist-vegan food, called "Jay" food in Thai. This is a useful word to learn if you're vegetarian. :) Jay food is more strict that vegetarian, it doesn't allow for ANY animal produce (dairy, etc.) and even doesn't allow things like garlic or onions! Does it still taste good then you may wonder: hell yea!
Almost any town of some size will have one or more Jay restaurants, learn to recognize the Thai or Chinese word for 'Jay' (see middle picture). Chiang Mai has quite a few of course, today I highlight Mata Restaurant. It is close to Central Department store. When you get to the North Western city corner (Jaeng Hua Rin) you would turn left to go to Central. Instead you continue straight on and find this place on the right hand side. Try some of the meat-like substitutes made from mushrooms and other ingredients. The 'duck' is excellent. :) Mata is not necessarily better than other places, but it's a bit bigger and has a little garden with a fountain. It also sells vegetarian snacks and groceries. 2 dishes 'over rice' will set you back 20 baht, or order a 'set' as pictured for 35.
Another place worth mentioning that is 'regular' vegetarian is http://chanchao.fotopages.com/?entry=74916(Khun Churn). They do an all-you-can-eat lunch buffet for 59 baht, AND it's open in the evening in really nice semi-outdoors restaurant setting. Khun Churn Restaurant relocated last year to Nimmanhaemin soi 5 (or 7?), down from soi 11 which still shows on many maps.