The Niggun "Vayehi Biymei Achashveirosh" is a Niggun on the first Possuk of the Megillah.
The Niggun in its original form is a cheerful tune without words.
Some say that the words were added to the Niggun after a Bochur came down from the small Zal to the Shalash after drinking Mashkeh while he was matching the words of the Megillah to the Niggun.
Chasidim adopted this lively and joyful Niggun that expresses the atmosphere of Purim to these words. Every year they would start singing this Niggun in front of the Rebbe when he entered 770 on Shabbat Mevarchim Adar, and the singing continued as the Rebbe encouraged the tune. Throughout the month they would sing the tune a lot in front of the Rebbe, especially at the Rebbe's gatherings on Purim.
At the Purim gathering of 5728, the Rebbe said: "...It is proper and fitting that there should be a tune that is especially for Purim - in the way that there is among Chasidim the Niggun "Podoh Besholom" that is connected with Yud-Tes Kislev, and in this way Niggunim that are connected with "Hakofos", and in this way Niggunim that are connected with Pesach and so on. However, for these needs someone who composes Niggunim, and this is not my "profession"... So, I searched in the Torah, maybe I can find from what is already prepared a Niggun that is connected with Purim, and indeed - without too much effort - I found: In Meseches Megillah, in the explanation of the Posuk that explains what Purim did for all the Yidden - "The Jews had light and joy and gladness and honor", it says: "Joy is holiday, as it says: 'And you shall rejoice in your festival'". And from this it is understood, that the tune "And you shall rejoice in your festival", has a special connection to Purim". - Later, the Rebbe said: "And since there is already a tune that was composed on the words "And you shall rejoice in your festival", until they compose a special tune for Purim, it will be this "And you shall rejoice in your festival" (which is brought in the Gemara for the matter of "The Jews had light and joy etc.") with the tune on these words". And the Rebbe began to sing: "וְשָׂמַחְתָּ בְּחַגֶּךָ וְהָיִיתָ אַךְ שָׂמֵחַ".
In all the years they sang at Purim Farbrengens the Niggun "וַיְהִי בִּימֵי אֲחַשְׁוֵרוֹשׁ" without words until the 5740's. In 5742 5743 and 5744 they sang the tune with words and the Rebbe encouraged it, afterwards, in the last years they sometimes sang with words and sometimes without words.
This tune is an inseparable part of Purim for Chabad Chasidim.
וַיְהִי בִּימֵי אֲחַשְׁוֵרוֹשׁ הוּא אֲחַשְׁוֵרוֹשׁ הַמֹּלֵךְ מֵהֹדּוּ וְעַד כּוּשׁ שֶׁבַע וְעֶשְׂרִים וּמֵאָה מְדִינָה