A mixture of the words chill and relax
except it seems to be there two words multiplied so its a sort of extreme relaxing.
Can be used for when you are sitting in your garden on a summer evening with a beer listening to 'Time of the Season' by The Zombies.
Or if someone is having a major freaker and going ape shit at people you can tell them to chillax.
Originated in the Netherlands, where students (both foreign and Dutch) spent so much time chilling & relaxing that both regular words were simply not strong enough to describe the constant and intense state of relexation said students were in.
It is used the very same way as "to chill" or "to relax" but has a slightly stronger connotation.