The tradition of a legend in our possession says that Judah killed Esau.
When? When Isaac died, Jacob and (the chiefs of) the twelve clans went
to bury him; as it is written (Gen. xxxv. 29), "And his sons Esau and
Jacob buried him." In the Midrash it is, "And Esau and Jacob and his
sons buried him," which fits the legend better. Arrived at the cave,
they entered it, and they stood and wept. The (heads of the) tribes, out
of respect to Jacob, left the cave, that Jacob might not be put to shame
in their presence. Judah re-entered it, and finding Esau risen up as if
about to murder Jacob, he instantly went behind him and killed him. But
why did he not kill him from the front? Because the physiognomy of Esau
was exactly like that of Jacob, and it was out of respect to the latter
that he slew Esau from behind.
THE MIDRASHIM, _Midrash Shochar Tov_, chap. 18.