I looked in FamilySearch and Ancestry but didn't find his birth record.
I'd contact the Washington Town Clerk, www.washingtonnh.org/Pages/WashingtonNH_Clerk/vitalrecords
and ask about old birth records.
Another resource is the Washington New Hampshire Historical Society, www.ultimate.com/washington/whs/
Do you have a copy of his newspaper death notice? His parents names might be in it.
Also I think Chicago was issuing death certificates in 1901. His parents names will be on his death certificate if the Informant knew that info. Successful Searching!