During the rainy season and for as long as water levels stay high (July to December), long-tail boats make the journey between Chiang Rai and Tha Ton daily. It's a scenic trip, passing tracts of virgin forest, riverside monasteries, and villages of thatched huts with fishers casting nets in the shallows.
The travel time is anywhere from three to five hours, depending on river conditions and on how many stops are taken along the way. Each boat takes six to 12 passengers, but operators may be reluctant to depart if there are insufficient passengers; chartering the whole boat costs 2000B. You can also make the trip (much more slowly) upriver from Chiang Rai.