While no-one can definitively say when the chair was first invented, or whom invented it, I think it would be fair to say that it is based on an age old concept; that is, having something to rest upon. There are hints at the existence of the chair during the Egyptian and Sumerian times, however they later emerged more commonly as an indicator of status, reserved mostly for royal families and high-ranking officials. The throne is an early example of this, with only kings, lords and bishops allowed a crafted form of seat at all. The size, decoration and detail of the chair were also indicators of the importance of the person sitting in them.
In 1400BC, the Ancient Greeks were constructing chairs with four (usually wooden) legs, which was of their design. This style was adopted by the Romans, who began to introduce it in the territories they took over. By the mid 1650's, chairs were much more mainstream and were often upholstered to give a sense of comfort. This element was developed until the 1750's, when chair designers and carpenters realised that the comfort of the chair should be as important as the appearance. From this point, the designs began to embrace the contours of the body, and it has been said that the French had a great impact on the weight and comfortability of future chairs.
It is my guess that from the beginning of time, people would have been creating their own versions of chairs, be it a rock or a well shaped tree stump. Although the intentional manipulation and design of this concept came into existence much later, the idea is something which would have always been, and will continue to be, a human need. For this reason, there is a vast field of potential within the confines of what a chair is, and what a chair should be.