Reddit reviews How Race Survived US History: From Settlement and Slavery to the Obama Phenomenon

I'll attempt to tackle this question:

First, most historians would disagree with Chomsky in regards to the 20th century being the only time that African Americans had a chance of "entering" American society (despite the fact that they already inhabit American society, though we will give Chomsky a pass and assume he meant equitable access to meritocracy and large scale integration). For instance, many scholars, such as David Roediger, have written about the period of Reconstruction as one in which a multi-racial and inclusive society was possible, and the failure of this possibility is reflective of the prevailing influence of race, class, and the importance of the "wages of whiteness" in perpetuating racism and racial divide. If you are interested in this topic, I would recommend two of Roediger's influential works; The Wages of Whiteness and How Race Survived U.S History

In regards to Chomsky's statements on the Drug War, largely, I would agree. However, I would push them and state that the Drug War is part of a longer history dating back to Reconstruction in which the criminalization and institutionalization of African Americans was a means to control and subvert their population. Some historians have gone as far as to say that mass incarceration of African Americans has come to replace slave labor in the United States, as these prisoners (then and now) were forced to work for little to no wages for certain industries (picking cotton in the South for example). There are many scholarly articles and monographs on the subject, however, if you are interested in the post Civil Rights era I would recommend The New Jim Crowe as an a starting point.

In regards to the last fact, I suppose the claim is subjective to what one defines as "freedom". However, many historians have demonstrated that whatever "freedom" blacks have gained throughout their history, it has always been subjected and juxtaposed with the unequal access to particular rights, liberties, and resources available to whites. George Lipsitz has written that public policy and private prejudice has been intertwined throughout American history, leading to tangible benefits for whites in terms of education and employment and an "investment" in whiteness against Blackness. Moreover, Du Bois wrote in Black Reconstruction that whiteness provided particular "psychological and public wages" that promoted racial prejudice and racial stratification. It is through this paradigm in which Chomsky's statements must be viewed. Largely I agree with his statements, though I wish he would preface them with the scholarly and theoretical underpinnings in which I have attempted to provide you. If you are interested in the subject, I would highly recommend reading Lipsitz's work that I have linked and Roediger's How Race Survived U.S history as an entry point.

There's an awful lot at that link, and I don't have time to go through all of it. But I hope a few suggestions for sources will be helpful to you anyway.

David Roediger's How Race Survived US History is readable and (like the article you linked) aims at a sweeping history of race and whiteness in the US.

Cheryl Harris' article "Whiteness as Property" is also a broadly-focused piece, and one that's inspired a lot of conversation. You'd need to have access to the Harvard Law Review and a willingness to push through some technical language, but it's worth it.

Harris, Cheryl I. “Whiteness as Property.” Harvard Law Review 106, no. 8 (1993).

I hope that helps.