I don't know how to delete my previous message so I am posting this by way of correction/addition. Just this week I received my g-g-grandmother's (Lydia O. CHASE Chambers) death certificate that I had sent away for and it listed her father as BELA Chase. This blew apart my whole theory but I went back and dug out that Bible and found out my memory had been rather faulty when I posted what I did. Instead of it being Lydia writing "my brother" on that clipping, it said "Mr Chase - my grandma's brother" in my grandmothers's writing. My grandmother was 59 years younger than Lydia so it is possible she was mixed up.
I also went and checked the census' in Oakland County.
A. Bela Chase had one female in his household of age "10 & under 15" in 1830. Lydia would have been ten in 1830.
B. Peter Chase has one female in the 1830 Census under 5 years of age (May Jane? born 1828), and one female 20 and under 30 (Elizabeth Cramer, born 1802). Peter did not have a female 10 & under 15.
Given the evidence of the death certificate, and the circumstance that the 1830 census seems to bear that out, it would appear that Lydia's father was indeed Bela and not his brother Peter. If this is the case then my grandmother, Ethel Chambers, was indeed mistaken about Thomas C. Chase (son of Peter) being Lydia's brother.
Other items of interest: The Chambers (Elihu & Lydia) land was in the upper corner of Section 16, Alpine Township. The Abel Chase (son of Bela) land was in the lower part of Section 16, Alpine Township. The Rachel Chase land (last wife of Bela) was in Section 16, Alpine Township.
Bela Chase is buried in the old Alpine Center Cemetery. Elihu & Lydia are buried in the old Alpine Center Cemetery.
One census shows William Chase and Albert Chase (other sons of Bela) as young men LIVING with Lydia & Elihu.
All of this points to the likelihood of Bela, not Peter, being Lydia's father.
New Hypothesis: If the given name of Bela's first wife, Orilla Whipple, was spelled Orilla and not Aurilla, would it not be a short leap of faith to surmise that the O in Lydia O. Chambers might stand for Orilla, her mother?