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We went in 2009 when England played Ukraine in a qualifier for the 2010 World Cup.
We set off about 10am (I think) from central Kyiv.
Bus ride to exclusion zone takes a couple of hours and gets bumpy as hell!
It cost about £80 each but we went in a group of about 40-50.
When we got there they served us lunch, some of which was tasty, some of it was awful. There was a LOT of it anyway. We were all a bit paranoid about eating stuff that might have been prepared in irradiated water! Apparently it's all piped in from a fair distance away though.
We then got taken to a few different sites closer, and closer to the reactor that blew. The guide showed us the readings on his geiger counter at each site.
At one point we stopped on the bridge near the reactor and you can see loads and loads of fish in the coolant canal. They're inedible so they just grow and grow in numbers.
Closest we got to the reactor was about 100 meters away. We couldn't stay too long there due to the severe radiation levels.
Then we went to Pripyat and got to wander around and explore. I didn't touch anything there with my bare skin but some of the lads has a kick about with an irradiated football. Real smart...
It was pretty spooky and certainly was sad. There's not masses to do except collect your thoughts and think about the poor souls who were in the mixer. Also it's a bit crazy to see a town deserted like that. We picked up a few cheap beers from the local shop (50p for a pint bottle). Afterwards we had to go through a radiation detector to make sure we weren't glowing too much and then we got the bus home. By the time we got back to central Kyiv it was about 6-7pm I guess.
If you're interested in doing it then go for it, but make sure you do lots in Kyiv too as that city is excellent. I really enjoyed it there - the Chernobyl/Pripyat trip was an interesting added different day out.
P.S. the food and beer in Ukraine was generally terrific.