|“||They swore an oath which none shall break, and none should take, by the name even of Ilúvatar, calling the Everlasting Dark upon them if they kept it not...||”|
The Oath of Fëanor was an oath taken by Fëanor and his seven sons after Morgoth killed Finwe and stole the Silmarils. In the first age this oath would be the greatest cause of strife between the Noldor.
Learning of his father's death at the hands of Morgoth, Fëanor went back to Tirion, breaking the exile set by the Valar. At Tirion, Fëanor gave an impassioned speech in which he convinced the vast majority of the Ñoldor to follow him to Middle-earth to wrest the Silmarils back from Morgoth and avenge Finwë. At the end of his speech, still drunk on rage, Fëanor swore the dreadful oath to Eru, calling Manwë and Varda in witness. His seven sons jumped to his side and swore the oath with him. 
The oath commanded Fëanor to press to Middle-Earth and resulted in the first kin-slaying at the havens of the Teleri. Fëanor died soon after his return to Middle-Earth but the remaining oath-takers, his sons, lived on in relative harmony with the Eldar of Beleriand.  For the greater part of the First Age, the oath kept the sons of Fëanor united in one cause to defeat Morgoth and retrieve the jewels.
However, the true dangers of the oath became apparent when Beren and Lúthien recovered one of the jewels from Morgoth. The presence of the Silmaril awoke the oath and caused the brothers to make war on the Elves of Beleriand because Dior, Thingol's heir refused to yield the jewel. The brothers attacked Doriath and sacked the halls of the Sindar, committing the second kin-slaying. However, the Silmaril escaped the destruction of Doriath and the oath drove the sons onwards. When they learned that it was possessed by Elwing, who dwelt near the mouths of Sirion, they attacked the defenseless exiles of Gondolin and Doriath, committing the third and most terrible kin-slaying.
But the Silmaril escaped them again and was borne by Eärendil into the West. That Silmaril was lost to the sons of Fëanor but two more remained inside the crown of Morgoth. So after the War of Wrath the two remaining oath takers, Maedhros and Maglor, stole the two Silmarils from the camp of the victorious west. However, due to the terrible deeds committed by the brothers in their retrieval of the Silmarils they found they could not handle the Silmarils without enduring searing pain. The two brothers parted and in his anguish Maedhros thrust himself and his Silmaril into a fiery chasm. Maglor on the other hand tossed his Silmaril into the sea and is said to wander the coast lamenting his loss and pain.
The Oath itself, as given in The Lays of Beleriand, is as follows:
“Be he foe or friend, be he foul or clean
Brood of Morgoth or bright Vala,
Elda or Maia or Aftercomer,
Man yet unborn upon Middle-earth,
Neither law, nor love, nor league of swords,
Dread nor danger, not Doom itself
Shall defend him from Fëanáro, and Fëanáro’s kin,
Whoso hideth or hoardeth, or in hand taketh,
Finding keepeth or afar casteth
A Silmaril. This swear we all…
Death we will deal him ere Day’s ending,
Woe unto world’s end! Our word hear thou,
Eru Allfather! To the everlasting
Darkness doom us if our deed faileth…
On the holy mountain hear in witness
and our vow remember,
Manwë and Varda!" 
- ↑ 1.0 1.1 1.2 The Silmarillion, Quenta Silmarillion, Chapter IX: "Of the Flight of the Noldor"
- ↑ The Silmarillion, Quenta Silmarillion, Chapter XIX: "Of Beren and Lúthien"
- ↑ The Silmarillion, Quenta Silmarillion, Chapter XXII: "Of the Ruin of Doriath"
- ↑ 4.0 4.1 The Silmarillion, Quenta Silmarillion, Chapter XXIV: "Of the Voyage of Eärendil and the War of Wrath"