From a reader:

Not only had he expressly disputed the term conservative, but he also saw the term as being contradictory. There was nothing conservative about overthrowing liberal hegemony. In this he was joined in early National Review years by James Burnham who felt there was something to that idea. There was, in addition to this, his criticism of Rand which was precisely what National Review had wanted from Chambers. The truth is that Chambers saw the Right as cognizant of a higher authority, and felt that capitalism was only the method by which a better society might be achieved. Rand focused, of course, on the self, and that self-centered universe wasn’t completely incompatible with conservatism as it stood. Thus Chambers wanted to keep his distance.
Chambers’s philosophical differences with the National Review editors did create a bit of friction, as I recall in my readings.