The Shulhan Aruch mentions the well-known custom to set aside a special chair at a Berit Mila designated for the prophet Eliyahu, who is known as "Mal’ach Ha’berit" ("the angel of the covenant"), and who, as tradition teaches, attends every Berit Mila that is performed.
Different explanations have been offered for why Eliyahu attends every Berit. Some explain that this is Eliyahu’s reward for the time when his soul was in the body of Pinhas, and he killed Zimri who committed an act violating the Berit Mila. In reward for Eliyahu’s zealotry in defending the purity of the Berit, he attends every Berit Mila. This is the explanation offered by the Perisha (Rav Yehoshua Falk, 1555-1614). From the Zohar, however, it appears that to the contrary, Eliyahu is forced to attend every Berit as a punishment for sharply criticizing the Jewish People before G-d, accusing them of rejecting the covenant. G-d reacted sternly, decreeing that Eliyahu would be forced to attend every Berit to see with his own eyes the Jews’ steadfast devotion to the covenant. Interestingly, the Arizal (Rav Yishak Luria of Safed, 1534-1572) adds that attending every Berit is considered a punishment for Eliyahu because the righteous souls in the heaven spend their time learning new Torah insights. Every time Eliyahu attends a Berit, he misses new precious insights into Torah, and this is his punishment.
Where should this special chair – the Kiseh Shel Eliyahu – be placed?
According to the consensus among the Halachic authorities, Eliyahu Ha’nabi’s chair should be placed to the right of the Mohel as he faces the Sandak who holds the baby. The right side, of course, is always considered the more prestigious side, which is why, for example, when somebody is walking alongside a Torah scholar, he should stand to the left of the scholar. Therefore, it is proper to position the Kiseh Shel Eliyahu to the right of the Mohel. Sometimes this is not a convenient location, as the Mohel might want to position his table of supplies on his right side, but when possible, this is where Eliyahu’s chair should be placed. Of course, if this is not possible, then the chair may be positioned elsewhere.
The Zohar teaches that a verbal announcement must be made designating the chair as the Kiseh Shel Eliyahu. If an announcement is not made, the Zohar writes, then Eliyahu does not attend the Berit. It is therefore customary for the Mohel to announce before performing the Berit that the special chair is designated for Eliyahu, and to pray that Eliyahu should soon appear together with Mashiah.
Summary: It is customary to designate a special chair for Eliyahu Ha’nabi at a Berit. The Mohel must announce that this chair is designated for Eliyahu. Preferably, the chair should be positioned to the right of the Mohel.