Just searching for Chester on his own without dates or parents gives over 150 trees.
I cannot vouch for the accuracy of any of them.
Googling '"chester alan arthur" genealogy' gives a number of hits that you may find useful as will '"chester alan arthur" ancestors'
I hope this information will set you on the right path.
Chester is the 2nd cousin 5X removed of a colleague of my daughter, and he cropped up when I was trying to find out she and the colleague were related, which they are - distantly via one marriage about 5 generations back. He's a curiosity as far as I'm concerned who is not as well researched as you might think.