The Chair of Eliyahu
Answer: In this week's Torah portion we learn of the appearance of G-d to our Forefather Avraham in connection with his undergoing Brit Milah. In his commentary Rabbi Ovadia Seforno suggests that since this was a covenant between G-d and Avraham, the Divine partner to this covenant was actually present at the circumcision. And since this covenant is renewed at every circumcision, he concludes, a chair is placed as if to welcome the Divine Presence.
Although this would suffice as a reason for placing an empty chair, the more widely accepted reason for this custom is based on a Midrash. When the Prophet Eliyahu spoke critically of the Jewish People whom he accused of abandoning G-d, he was ordered by G-d to attend every Brit Milah and to report it as a proof of Jewish loyalty to their G-d. This is why we call that empty chair upon which we place the child at the beginning of the ritual "Eliyahu's Chair".
Although many Jews in our own time are deserving of Eliyahu's ancient criticism, the fact that they still arrange a Brit Milah for their sons allows Eliyahu to bring to Heaven a favorable report.