When I first came to Chiang Mai I stayed at Doi Suthep for 3 weeks. Meditating. Not being the worlds best meditator I spent most of my time chatting to the staff and monks there. They believed that the relic (part of Buddhas Shoulder) is a magical clone of the relic at Wat Phra That Harapunchai in Lamphun. There's probably a story about averting a war or ratifying a treaty between the two cities behind that. The original relic came via Sukothai, I don't know where it came from before that, never checked, the monks weren't particularly interested in that aspect, sadly. It's not particularly impressive, a solid glass ball with some bits of bone inside. Normally in these relics the bone is fused with the glass making it difficult to extract them with smashing everything.
Lady Hawk, if you go to the library in Doi Suthep you can ask to see "Tamnin Phra That Doi Suthep', the Chronicle of the Chedi, apparently all the details are in there. A much more accessible read (ie, it's in English) is "Sacred Mountains of Northern Thailand and Their Legends", by Donald Swearer, published by Silkworm.