What is the special connection between Aharon and the holiday of Chanukah?

הִלֵּל וְשַׁמַּאי קִבְּלוּ מֵהֶם. הִלֵּל אוֹמֵר, הֱוֵי מִתַּלְמִידָיו שֶׁל אַהֲרֹן, אוֹהֵב שָׁלוֹם וְרוֹדֵף שָׁלוֹם, אוֹהֵב אֶת הַבְּרִיּוֹת וּמְקָרְב לַתּוֹרָה

(פרקי אבות א:י"ב)

Hillel and Shammai received [the oral tradition] from them. Hillel used to say: be of the disciples of Aaron, loving peace and pursuing peace, loving mankind and drawing them close to the Torah. (Pirkei Avot 1:12)

"Be of the disciples of Aharon, loving peace and pursuing peace"
When Aharon would see two people quarreling, he would go to each one of them without the knowledge of his fellow and say to him, “Behold how your fellow is regretting that he sinned against you; and he told me that I should come to you so that you will forgive him.” And as a result of this, when they bumped into each other, they would make peace with one another.
(Avot DeRabbi Natan)

The Chassidic Masters describe Chanukah as a “holiday of love”.  Sadly, in the days of Chanaukah there developed a great divide within the Jewish people . They broke down into two groups Yehudim (Jews) and Mityavnim (Jews who had adopted a Greek lifestyle). The miracle of Chanukah inspired the Jewish people to unify once again!

Aharon Hakohen was the first to ever light the Menorah. It seems most fitting that he be the figure to represent the ‘Holiday of Peace and Love.”