In reply to The New NickB:
I did it solo in two, two day sections with a day off in Chamonix in between in early August 2015. I took the early morning bus to Courmayeur and did the Champex - Col De Balme - Chamonix side anti-clockwise, then a couple of days later took the early morning bus back to Courmayeur again and did the other half clockwise.
My approach was to carry lightweight camping kit and walk until the early evening, stop, pitch up and eat, and then get up early the next morning to repeat the process. Most of the huts I passed looked rammed, and there was a lot of traffic around them as people arrived for their stay, but I often saw hardly anyone else on the the trail after about 5pm, and I was also on my own for a couple of hours each morning as well. I planned it so that I pitched my tent high up, staying just below the Col Des Fours and the Fenestre D'Arpette (on the Champex side). What with carrying about 12 kg of kit and food / water I was on my feet for most of the day, which were in a sorry state by the time I got back to Chamonix.
Great walking over most of the route, although I recall finding the Val Ferret to be a bit of a bore. It was a great experience and the route isn't at all intimidating. (Which is more than I can say about some of the follow up 'bivi walks' I did, as with my trip around Mt Buet via the Frêtes du Grenier. Mt Buet itself is the biggest pile of scary choss I have ever been up, and overnighting in the Combe de Buet was like camping on the moon.)