It was King Phayo the fifth king of the Mangrai dynasty that founded Chiang Mai, who started the construction of Wat Phra Singh in 1345. Later came all the other buildings.
The reason why he wanted to build the temple, is the same reason as to why many other temples were built in Chiang Mai. He wanted to build a chedi for his father’s ashes.
First was the temple named Wat Lichiang Phra. In 1367, a Buddha statue of Phra Buddha Singh was brought to the temple. Then the name was changed to the name we know today Wat Phra Singh.
The statue according to legend came from Mahabodhi Temple of Bodh Gaya in India and was first brought to Thailand via Sri Lanka. First to Nakhon Si Thammarat and later to Chiang Mai.
The temple is located in the western part of the city, inside the moat and the city walls. In front of the temple, there are 2 big stone lions, there guard the entrance.
I can only recommend a visit to Wat Phra Singh, it is rather big and there is a lot to look at.