Map from Google - Ko_Chang

In Koh Chang, and in 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 a tropical cyclone can still pass (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 744 metres (2,440 feet), and are covered by a rainforest. The rivers that originate from these hills give rise to several waterfalls, including those of Klong Plu.
The temperature is high throughout the year, so that the average highs never drop below 30 °C (86 °F). However, from December to March the humidity is slightly lower. During the night, temperatures rarely drop below 20 °C (68 °F), although this can sometimes happen 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 (together with May, the first monsoonal month) are usually the hottest months of the year, in which highs can quite often reach 35/36 °C (95/97 °F).
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
TratJanFebMarAprMayJunJulAugSepOctNovDec
TratJFMAMJJASOND
Min (°C)202223242424242424232221
Max (°C)313233333231313031313131
Min (°F)687273757575757575737270
Max (°F)889091919088888688888888

In Koh Chang, an average of approximately 3,500 millimetres (138 inches) 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 (20 in) per month.
This is the average rainfall in Trat.
Average precipitation - Trat
TratJanFebMarAprMayJunJulAugSepOctNovDecYear
TratJFMAMJJASONDY
Prec. (mm)25558012035062558073054531090203525
Prec. (in)12.23.14.713.824.622.828.721.512.23.50.8138.8
Days3571121232425241993174

The amount of sunshine in Koh Chang is quite good in the dry season, from November to April, while during the rainy season the sunshine alternates with cloudiness, which can be more or less durable, and can lead to rain showers. In August, the rainiest month, the sun is rarely seen.
Sunshine - Trat
TratJanFebMarAprMayJunJulAugSepOctNovDec
TratJFMAMJJASOND
Sun (hours)766654424567

Koh Chang like can be affected by tropical cyclones, in particular from typhoons, which come from the east, normally from June to December (although they are more frequent from September to November), and generally affect more directly the interior of Thailand, but sometimes they can also enter the Gulf of Thailand.

White sand beach, Koh Chang

For swimming, the sea is warm all year round, as you can see in the following table.
Sea temperature - Ko Chang
Ko ChangJanFebMarAprMayJunJulAugSepOctNovDec
Ko ChangJFMAMJJASOND
Sea (°C)282829303030292929292928
Sea (°F)828284868686848484848482

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 the rains are already rare, 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.