Augustine of Hippo (354-430 AD) is credited with the presentation of this argument for the existence of God.  Augustine reasoned that since man was created in the image of God (Genesis 1:26), this left intuitional consciousness about God's existence.  According to Stewart¹, Augustine used the following two Scriptures as evidence of this argument:

11 He has made everything appropriate in its time. He has also set eternity in their heart, yet so that man will not find out the work which God has done from the beginning even to the end. Eccl 3:11 (NASB)

14 For when Gentiles who do not have the Law do instinctively the things of the Law, these, not having the Law, are a law to themselves, 15 in that they show the work of the Law written in their hearts, their conscience bearing witness and their thoughts alternately accusing or else defending them, 16 on the day when, according to my gospel, God will judge the secrets of men through Christ Jesus. Romans 2:14-16 (NASB)

Note that "instinctively" in Romans 2:14 is also translated "by nature" in some other English versions, and both of these are reasonable translations of the Greek word according to BAGD.²

These Scriptures appear to suggest that there is something within the nature of man that is somehow influenced by the Almighty God.  For those who believe that the Bible is the Word of God, this proposition is not difficult to accept.  However, for those who reject the Scriptures as the Word of God, these Biblical passages have no significant meaning, and are not empiric enough to establish the fact of God to them.

Now in regard to the second Scripture reference, other champions of the idea that there is a moral law within man arose in people such as Immanuel Kant (1724-1808 AD).  Kant was a philosopher and his concept of the moral law within was that of a universal law that is applicable to every person because every person would agree that it is good.  A summary of Kant's moral order is as follows:

The summum bonum (Highest Good) is where moral virtue and happiness coincide.
We are rationally obligated to attain the summum bonum.
What we are obliged to attain, it must be possible for us to attain.
God (or the afterlife) must exist.³

In this same reference, atheists such as Friedrich Nietzsche disagree with Kant and say that a moral order can arise without a god, and that the conclusion that God exists is unnecessary.  Thus, Kant's attempts to demonstrate a moral law within man are vain in their eyes.

C. S. Lewis (1898-1963) was a modern champion of this idea of a moral law within man.  Lewis felt strongly that this moral law within man testifies to the existence of God.  His book entitled Mere Christianity still remains in print and available through multiple sources including www.amazon.com .  If you are interested in pursuing Lewis' presentation of the moral law within, then I urge you to read Mere Christianity for yourself.  Lewis is perhaps the best modern advocate for this position since he presents the concept without the usual religious jargon that frequently confuses people.