#60 Oath Genesis 24

Now Abraham was old, well advanced in age; and the Lord had blessed Abraham in all things. So Abraham said to the oldest servant of his house, who ruled over all that he had, "please put your hand under my thigh, and I will make you swear by the Lord, the God of heaven and the God of the earth, that you will not take a wife for my son form the daughters of the Canaanites, among whom I dwell; but you shall go to my country and to my family, and take a wife for my son Isaac." And the servant said to him, "perhaps the woman will not be willing to follow me to this land. Must I take your son back to the land from which you came?" But Abraham said to him, "beware that you do not take my son back there. The Lord God of heaven, who took me from my father's house and from the land of my family, and who spoke to me and swore to me, saying, 'to your descendants I give this land,' He will send His angel before you, and you shall take a wife for my son from there. And if the woman is not willing to follow you, then you will be released from this oath; only do not take my son back there." So the servant put his hand under the thigh of Abraham his master, and swore to him concerning this matter. Genesis 24: 1-9

As the oldest servant, Eliezer would have been the first in line to inherit Abraham's possessions if he would have had no children. 

Abraham stresses the seriousness of the task he is asking his servant to perform by having him participate in a formal oath. He invokes the name of God, that his servant understand that this between them, before the God of heaven and earth. He has Eliezer put his hand under his thigh which is apparently a gesture signifying that the oath taker understands he is in a covenant and accepts the responsibility to perform what is asked of him. 

The contact has one clause of release, and that is if the girl refuses to return with the servant. Abraham seems confident that this is in God's will as he declares that His angel will go before the servant.