Promises alone don't make a binding contract, but you don't need notaries or witnesses either. A legal contract is an agreement that is enforceable by law. Generally, the law enforces an agreement if one party makes a promise in exchange for valuable consideration to be given by another party.
For a contract to be legally enforceable, several conditions must be met. The parties to the contract must be competent adults, the subject of the agreement must be legal, the exchange must be based on valuable consideration and the contract must represent a "meeting of the minds," signifying mutual assent. It is not always necessary that the agreement be in writing.
Oral contracts are generally enforceable if the terms can be carried out in less than a year. Some contracts, however, must be written to be enforceable. These include agreements involving the ownership of real estate and sales contracts for goods worth $500 or more. No general requirement mandates that a contract be notarized or witnessed in any way to be binding.