Hi, and a warm welcome to Rootschat!
What is the source of the 1886 birthdate and Chester birthplace for William? Have you found him on a census?
There are a lot of births for William Wrights arund that time and in that area - but if it is exactly 1886 and Chester, and no middle name, then how about:
Jul/Aug/Sep 1886 Chester Reg District, ref 8a 422, William Wright, mmn Ballaher