A SQL join seems much simpler here. Assuming you've set up navigation properties correctly, that would look a bit like this:
from a in db.TableA
where a.TableB.TableC.C_Number == "10001"
select a;
Or in fluent syntax:
db.TableA.Where(a => a.TableB.TableC.C_Number == "10001")
The corresponding SQL would be something like this:
SELECT a.*
FROM TABLE_A a
JOIN TABLE_B b ON a.TABLE_B_REF = b.TABLE_B_REF
JOIN TABLE_C c ON b.TABLE_C_REF = c.TABLE_C_REF
WHERE c.C_NUMBER = '10001'