ANSWER: The promise of the rainbow is found in the 9th chapter of Genesis.
And God said, “This is the sign of the covenant that I make between me and you and every living creature that is with you, for all future generations: I have set my bow in the cloud, and it shall be a sign of the covenant between me and the earth. When I bring clouds over the earth and the bow is seen in the clouds, I will remember my covenant that is between me and you and every living creature of all flesh. And the waters shall never again become a flood to destroy all flesh. When the bow is in the clouds, I will see it and remember the everlasting covenant between God and every living creature of all flesh that is on the earth.” God said to Noah, “This is the sign of the covenant that I have established between me and all flesh that is on the earth.” (Genesis 9:12-17 ESV)