Also, Joel Whitburn's book "The Billboard Book of Top 40 Hits" is in its 8th edition (published 2004). It's considered by many to be the definitive book and is (obviously) sanctioned by Billboard.
There are also variants out there by him and others (TBBO Hot 100 Singles, TBBO Top 10 Singles Charts, Billboard Top 1000 Singles, etc.; check amazon.com for more). You can almost certainly find the Book of Top 40 Hits at your local library in the reference section.
You probably won't find anything online that's free.
(Note: I know this has been discussed before in the Wienerboard days, but I couldn't find it with a search)
While not in chronological order, billboard used to have this thick ass book that listed every artist's appearance on the top 200 album chart, which was THE bible back when I was a chart geek, but it was just a little south of 100 dollars.
Billboard might still have the top half of the albums charts and singles charts going back at 5 year intervals for free on their site. Which is fun, because you get to see western civilization devolve at the click of a mouse.
Thom Yorke is putting out a solo album. (usatoday.com) ...but he says he had the bands permission to do so, so there's no worries of him getting a big head or anything. It's not like he's Gwen Staffani or anything. It drops in July.