The Thais really haven't fought a war on their home soil since the 1700's. The Karen hill tribes however have been in a constant state of at least disarray if not war since the 1600's. The Karen were the first people to settle in what is now Burma and when the people who settled in the southern part extended their rule, the fighting started. The Burmese have never wanted the Karen and the Thais have never wanted them either. The designation of borders between Burma and Thailand in the mid 19th century cut across Karen communities with no regard to the populations. Karen who have lived in Thailand since that time were never recognized as Thais until recently.

In recent years there has been a "War" between the Burmese government and a group of Karen Christians that is eerily similar to the LRA/Uganda problems. You can read a bit about it here.