Sforno on Genesis 18:1/ספורנו על בראשית י״ח:א׳

1וירא אליו ה' באלוני ממרא, because this was where Avraham had circumcised himself at that time. His whole household had been circumcised with him at the time. This is where G’d manifested Himself as a sign that He stood by the covenant, similar to the verse at the beginning of Deuteronomy 29,9-11, commencing with the words אתם נצבים היום, and to Kings II 23,3 ויכרות לפני ה'. He appeared to Avraham seeing he was the individual most deserving to be the recipient of such a vision. We have a similar occurrence in Exodus 4,24 ויפגשהו ה', where G’d “met” with Moses without delivering an oral message. At that time G’d’s purpose was to ensure that Moses would circumcise his son, to maintain the covenant which was to be an eternal covenant with the descendants of Avraham as spelled out in Genesis 17,11-12. Perhaps this is the reason why a chair is prepared at the occasion of the circumcision (Pirkey de Rabbi Eliezer 29, as well as Zohar Bereshit 13,10) This chair alludes to the fact that hopefully, the presence of G’d will attend this marking of the sign of the covenant by a new member of the Jewish people.