Moab covered Fry's ill-spent teenage years, which were remarkably ill-spent; they ended with a two-year stint in prison for larceny. Chronicles picks up from there, with Fry teaching at a mid-rank public school and studying hard for his all-important college entrance exams. And either more strings were pulled than Fry lets on to, or he did extraordinary well on those exams, because he's soon firmly ensconced in Queens' College, Cambridge.
(Parenthetically, I know there must be plenty of people who went to Oxbridge colleges and then utterly failed in life -- became pathetic multiple bankrupts, or drug addicts, or otherwise pure drags on the body politic -- but every single story of British success seems to follow that precise path: did well on exams, got into elite college, met classmates who were amazingly helpful later in life, started doing {thing was later famous for} at college, got awards, graduated almost directly into professional success. Surely some of this is post-facto polishing, but it's still amazingly boilerplate when seen from outside.)
Fry apologizes incessantly for his successes, of course, in that very British way. He also apologizes incessantly for his faults and failures; Chronicles opens with two chapters about his life-long struggles with eating too much (particularly sweets) and with cigarettes. And, to make the whole thing even more meta; the book as a whole opens thus:
I really must stop saying sorry; it doesn't make things any better or worse. If only I had it in me to be all fierce, fearless and forthright instead of forever sprinkling my discourse with pitiful retractions, apologies and prevarications.
Chronicles is, inevitably, a book for Stephen Fry fans; who else would care? But it does cover the whole of the '80s, from those three years at Cambridge through his first professional successes and on to the first bits of Fry and Laurie, and there's a lot of good work (Blackadder, Me and My Girl), and even more interesting not-quite-successes (too many to mention) in those years. It doesn't get him to his greatest professional successes -- QI, Jeeves & Wooster, Wilde, Making History, and so on -- but, in the way of so many show-business memoirs, it loses some energy as it goes along and the author/subject finds himself ever more successful, professionally and financially. (Although Fry does leave himself an opening for a third memoir: he hints very strongly at the end that he became addicted to cocaine at around the time Chronicles leaves off, giving him another struggle to write about in the future.)