Probably one of the best restaurants serving Southern Thai food is Phuket Laikhram, http://chanchao.fotopages.com/?entry=70782(see this review.) It's however a bit more of the Chinese style southern food like you'd actually find in Phuket town, and not the hard-core seriously spicy curry stuff. I think that type of food deserves mention of its own. I'm not entirely sure this place here is one of the best in Chiang Mai, but it is authentic, has good variety and is definitely very very spicy, as in: spicy by Thai food standards.. :-D
I've tried a few Southern Thai places the past few weeks, and they all seem to have one thing in common: operators try to warn a Western looking visitor about the spicy food, suggest non spicy dishes or even try to discourage him ordering some of the spicier stuff! 0) So bring some level of determination if you want to sample the spiciest of foods..
I'm still looking for 'The Ultimate Southern Thai' food in Chiang Mai, do comment if you know of a place, but for now this one will do. It's called 'Lung Jit' and is on Arak Road, this is the road along the city moat, on the inside, 100-200 meters after passing Hua Rin Corner and just before you get to the first U-turn that would lead you to Ram Hospital.