The Nagorno-Karabakh conflict was actually the one that broke the myth of peaceful coexistence of Soviet Union nations. Up to that point, you could still be wondering how that diverse mix of nations could last for over 50 years without significant national conflicts. Even if we know now that the Balts did not like too many Russians coming (and more visibly, started discussing greater economical and political independence), or that Caucasian and perhaps Central Asian nations did not like each other - there were hardly boiling developments noticeable. And yeah, people were telling jokes and anecdotes about other peoples - not so politically correct perhaps, but no one had the idea to hurt or provoke because of nationality. (Exceptions in the Army? For what we know, seniority was a bigger problem there.) Nagorno-Karabakh was a big shock to that perception.

As we know, the Armenian dominated Nagorno-Karabakh is inside the Azerbaijan territory, while Azerbaijan's Nakichevan is separated from the mainland by Armenia's piece:

That has the following history:

In April 1920, while the Azerbaijani army was locked in Karabakh fighting local Armenian forces, Azerbaijan was taken over by Bolsheviks. Subsequently, the disputed areas of Karabakh, Zangezur, and Nakhchivan came under the control of Armenia. During July and August, however, the Red Army occupied Karabakh, Zangezur, and part of Nakhchivan. On August 10, 1920, Armenia signed a preliminary agreement with the Bolsheviks, agreeing to a temporary Bolshevik occupation of these areas until final settlement would be reached. In 1921, Armenia and Georgia were also taken over by the Bolsheviks who, in order to attract public support, promised they would allot Karabakh to Armenia, along with Nakhchivan and Zangezur (the strip of land separating Nakhchivan from Azerbaijan proper). However, the Soviet Union also had far-reaching plans concerning Turkey, hoping that it would, with a little help from them, develop along Communist lines. Needing to placate Turkey, the Soviet Union agreed to a division under which Zangezur would fall under the control of Armenia, while Karabakh and Nakhchivan would be under the control of Azerbaijan. Had Turkey not been an issue, Stalin would likely have left Karabakh under Armenian control. As a result, the Nagorno-Karabakh Autonomous Oblast was established within the Azerbaijan SSR on July 7, 1923.