I can only assume Ron Chernow, among others, view Alexander Hamilton a product of the Enlightenment, a rationalist, or something less than an Orthodox Christian.
The idea that committing sin, or failure to proclaim Orthodox doctrine, is a false basis for understanding the heart of a person. If committing sin was the criteria, no one would pass the test. Rather, slavery to sin, is what God's Spirit will convict. Chernow and others, imply this view against Hamilton. It is not fair, nor accurate. Most Christians, including myself, are not members of a Church, just for the fact of not getting around to it; ironically, the same reason Hamilton failed to commune before his death bed.
Constitution Signer Rufus King wrote less about Christianity than Hamilton, yet his faith is not questioned. George Washington, and James Madison are viewed in the same light. Many Christians are silent about their faith, thus, never speak a word of Orthodoxy. I am not defending the faith of George Washington, however, James Madison is pigeon-holed the same way Hamilton is. The below quote should once and for all, refute Hamilton was a product of the Enlightenment, or viewed reason superior to anything. On the contrary, he viewed man's reason with the highest contempt:
Experience is a continual comment on the worthlessness of the human race; and the few exceptions we find have the greater right to be valued in proportion as they are rare.
-To Colonel Richard K. Meade, Albany, August 27, 1782.
That quote along with the one below, nearly proves beyond a doubt, Hamilton believed in Original Sin. He understood human depravity could never be corrected, unlike proponents of the Enlightenment. In the below statement, AH sounds identical to John Calvin:
As riches increase and accumulate in few hands; as luxury prevails in society; virtue will be in a greater degree considered as only a graceful appendage of wealth, and the tendency of things will be to depart from the republican standard. This is the real disposition of human nature: It is what, neither the honorable member nor myself can correct. It is a common misfortune, that awaits our state constitution, as well as all others..It is a harsh doctrine, that men grow wicked in proportion as they improve and enlighten their minds. Experience has by no means justified us in the supposition, that there is more virtue in one class of men than in another. Look through the rich and the poor of the community; the learned and the ignorant. Where does virtue predominate? The difference indeed consists, not in the quantity but kind of vices, which are incident to the various classes; and here the advantage of character belongs to the wealthy. Their vices are probably more favorable to the prosperity of the state, than those of the indigent; and partake less of moral depravity. [bold face mine]
-Alexander Hamilton, New York Ratifying Convention 21 June 1788. Papers 5:36--37, 40--43
Hamilton rented Pew 92 at Trinity Church as early as 1790, affirming at least his church attendance. He isn't on the Communion roll, but his wife is. As to taking Communion, he had desired it, yet accomplished it on his death bed:
It has for some time past been the wish of my heart, and it was my intention to take an early opportunity of uniting myself to the church, by the reception of that holy ordinance [Communion].
Who then can claim how long "some time past" is? Based on his Calvinist view of human nature, and his previous affirmation of the Trinity; the evidence supports Hamilton was an Orthodox Christian.