As your correctly pointed out, the Chin are one of the most Christianised ethnic group in Myanmar. A 1983 census revealed that 70% of Chin were Christians, and the figure could be close to 90 percent today. Observers believe that 90-95% of the Kachin, another ethnic group in Myanmar, are also Christian. A third of the Karen, yet another ethnic group in Myanmar, is also estimated to be Christian. In this reply I will focus on the case of the Chin.
So why is Christianity so popular with this group? To explain the conversion of the Chin people to Christianity, we first have to understand the dynamics between the different ethnic groups in Myanmar before the colonisation by the British.
If you look at a map of Myanmar, you will see that the country is dominated by a river which flows in the middle of the country, the Irrawady. It provides an easily navigable waterway and irrigates crops, which makes it suitable for a large population. The area in the plains around the Irrawady is mostly inhabited by Bamars (or Burmans), who are by far the largest group in the country. Bamars are also predominantly Buddhists. Throughout history, Bamar States, such as the Pagan Kingdom, the Taungoo Dynasty or the Konbaung dynasty rose to power and conquered the more scarcely populated highlands and mountainous areas surrounding the river, which are inhabited by other ethnic groups like the Chin, Kachin and Karen.
These areas were only loosely administered by these Burmese empires who ruled through the “Mandala system” where the influence of the State wanes the further one is from the centre. For examples, the Kachin paid both tribute to the Burmese king and the Chinese emperor in Beijing. These ethnic groups never converted en masse to Buddhism, but held various animist beliefs.
For the Chin, their tradition was known as phunglam, or “ways of life”. It was a monotheistic tradition based around the belief of a Supreme Being, souls, and life after death. From the start, their beliefs seemed to be quite compatible with Christianity, or at least more than those of Buddhists.
Following the three Anglo-Burmese wars in 1824-1826, 1852-1853 and 1885, the British gradually conquered all of present-day Myanmar. In the 1860s, the British started invading the Chin territories, which proved to be a particularly though area to conquer. The British found the Chin to be fierce and skilful fighters. By 1896, all of the territories had been conquered by the British. Even though British colonial authorities in Burma did not particularly welcome missionaries, in the case of the Chin, they believed that converting them to Christianity would make them more docile and ready to accept rule from the colonial administration. Reverend Arthur Carson and his wife Laura from the USA were the first missionaries to arrive in the area. They were later joined by a medical missionary, Dr E.H. East.
The Chin gradually converted to Christianity, in part because it was compatible with their animist beliefs, and also for the work provided by the missionaries to develop their society. The missionaries helped develop a written Chin language, which did not exist before. The unification of the disparate tribal groups inhabiting the Chin hills into a single Chin identity made Christianity even more attractive. Over time, Christianity became inseparable from Chin identity.
My sources for this comment are :
Burma, a Nation at the Crossroads by Benedict Rogers
Burma/Myanmar, What Everyone Needs to Know by David I. Steinberg