Map from Google - Ko_Chang

In Koh Chang and the nearby islands of Ko Mak and Ko Kut, the climate is tropical, hot all year round, with a rainy season, due to the southwest monsoon, which runs from May to October and in this area is felt in a remarkable way, and a dry season from December to April. In March and April, before the monsoon, there is a certain rise in showers, while in November there may still be the passage of a tropical cyclone (see below).
Koh Chang, whose name means "Elephant Island", is located in the Gulf of Siam; it is the second largest island of Thailand, and is protected, along with the surrounding islands and the coral reef, in the Mu Ko Chang National Park. In the interior of the island there are some hills, which reach up to 744 metres, and are covered by a rainforest. The rivers that originate from these hills give rise to several waterfalls, including those of Klong Plu.
Temperatures are high throughout the year, so that average highs never drop below 30 degrees. However, from December to March the humidity is slightly lower. During the night, temperatures rarely drop below 20 degrees, although this may happen sometimes between December and March. From February to April, before the arrival of the monsoon, there is a slight rise in temperature, so that March and April (along with May, the first monsoonal month) are usually the hottest months of the year, and in which highs can quite often reach 35/36 degrees.
Here are the average temperatures of the nearby city of Trat, which is located on the mainland and is the capital of the province.
Average temperatures - Trat
Trat J F M A M J J A S O N D
Min (°C) 20 22 23 24 24 24 24 24 24 23 22 21
Max (°C) 31 32 33 33 32 31 31 30 31 31 31 31

In Koh Chang, an average of approximately 3,500 millimetres of rain falls each year; as mentioned we are in an area where the rains in the monsoon period are particularly abundant, because the south-western winds hit it directly. From June to September, precipitation exceeds even 500 mm per month.
This is the average rainfall of Trat.
Average precipitation - Trat
Trat J F M A M J J A S O N D Year
Prec. (mm) 25 55 80 120 350 625 580 730 545 310 90 20 3525
Days 3 5 7 11 21 23 24 25 24 19 9 3 174

The amount of sunshine in Koh Chang is good in the dry season, from November to April, while during the rainy season the sun does not fail, but it alternates with some cloudiness, which may lead to rain showers: there are on average 9 hours of sunshine a day in December and January, 8 in November and from February to April, 6 in May and October, and only 5 from June to September.

From May to November, Koh Chang like the rest of Thailand can be affected by tropical cyclones, although this area is relatively protected, since cyclones develop in two areas, one to the west (the Bay of Bengal, where they are called cyclones), and one to the east (the Pacific Ocean and the South China Sea, where they are known as typhoons); sometimes however some of them may pass even here.

White sand beach, Koh Chang

For swimming, the sea is warm all year round, as you can see in the following table.
Average sea temperatures - Koh Chang
Koh Chang J F M A M J J A S O N D
Sea (°C) 28 28 29 30 30 30 29 29 29 29 29 28

When to go

The best time to go to Koh Chang for a beach holiday goes from December to March or April, being the dry season. In November, usually it already rains little, but as I said a tropical cyclone can still pass, while in March and April it's hot and the pre-monsoon rains become more frequent, so the best time of all is from December to February.