The first bicycles to use pedals had no chains.
Later, as the ability to make small but strong steel parts was developed, so were chains, but the first bicycles to use these has one on each side of the bike.
In 1889, Harry John Lawson made the first bicycle driven by a chain to the rear wheel. This use only one chain and it was placed on the right hand side of the bike.
In 1885 John Kemp Starley produced the first rear wheel driven bicycle with equal sized front and rear wheels. IT was and it the basis of all modern bicycles. It became known as the "Rover".
It would seem there is no historical reason for the placement of the chain, other than Mr Lawson originally put it there, Mr Starley followed the idea, and the rest of the world copied him.
We can only speculate why Harry lawson put the drive chain on the right hand side of the bicycle.
He may have simply placed it there because that was the side he was standing at when he began to put it together.
it may be, as suggested to keep it out of the way for mounting the bicycle.
Possibly its because the majority would push off with their right foot and apply power more directly. Although this benefit would only be of any use when setting off.
It could possibly be that because the bicycle was hugely developed in Britain at this stage of its life, the chain was placed on the right to keep it away from the pedestrians on the left.
Whatever the reason, its been lost a long time.