I was quite stunned and surprised to read about this and thought it was worth sharing.
For the past 5 years, there seems to be some evidence reporting a strong connection between chronic sleep deprivation and ADHD. A research study published in the March 2002 issue of Pediatrics reported that children who snored were almost twice as likely as their peers to have ADHD. Large tonsils and adenoids can slightly block the airway passage at night, which leads to snoring, less sleep, and maybe ADHD. For children truly affected by obstructive sleep apnea and ADHD, the tonsillectomy may just be a cure.
More on this in the Dallas News, Healthbeat, and Fox News.

Comments
It is important to realise that the behavioural symptoms of ADHD are underlain by real neurological deficits. Tonsillectomy may ameliorate some of the symptoms, however it does not necessarily impact on the underlying neurology. Having my child’s tonsils removed has not in any way affected her primarily inattentive type ADHD and it also had no effect on my own ADHD. This is not a rational explanation for ADHD but is one approach which may work for some. Sleep problems in ADHD have many more manifestations than enlarged tonsils and adenoids.
If ADHD is to be managed well, then all factors affecting behaviour need to be examined.
When I got concerned about my son’s snoring and behavior patters I was told everything from ADD, ADHD, allergies, and sleep apnea. I never did any ADHD drugs, but tried numerous allergy medications and nothing worked. I read an article written by a Pediatrician in Tucson, AZ that believed tonsils and ADHD were related and fought with my Pediatrician for over a year. He stated we only take tonsils out of a handful of 40,000 kids we see each year and because my son was never sick he didn’t see a need to xray them. Once I saw an ENT and a CT was performed, the results indicated by son’s tonsils were 3X the size they should have been and his adenoids hanging down his throat. The Pediatrician called me that night and apologized. My son’s oxygen levels were at 74 before surgery and the surgeon told me he’s surprised he didn’t die in his sleep. After surgery they were between 96-98. 4 days after surgery I had to constantly check on my son because I couldn’t hear him breath with my face next to his. What a difference afterwards with his behavior and breathing. It may not be the cure for everyone, but I do believe there are a lot of kids on drugs that do not need to be. I’m just glad I saw the article I did.
I agree w/Calochilus & wanted to add that I had my tonsils removed when I was 6. There was NO observed difference in my ADHD. I grew into an adult w/ ADHD. I also want to note that my small frontal lobe and diveated septum: both discovered as an adult, may/may not also be part of the physical traits of those w/ADHD.