Consulta SQL para la cadena padre-hijo

Usa un CTE recursivo :

DECLARE @id INT
    SET @id = 3

;WITH hierarchy AS (
  SELECT t.id, t.parentid
    FROM YOUR_TABLE t
   WHERE t.id = @id
 UNION ALL
 SELECT x.id, x.parentid
   FROM YOUR_TABLE x
   JOIN hierarchy h ON h.parentid = x.id)
SELECT h.id
  FROM hierarchy h

Resultados:

id
---
3
2
1