Chicken Egg

It's not just a question of keeping the egg at the right temperature, though this is really important, but also providing the right humidity levels. In an incubator this will be controlled for you, and under a hen there will be the right amount of humidity from her body, but under a lamp it will be too dry and the chick wouldn't survive. Also the egg has to be turned several times a day, to help the chick develop properly. I also agree about the problems of buying fertile eggs on e-bay - some traders are genuine but many will rip you off, and in any case, once an egg has travelled to you in the post it's less likely to hatch as they don't like being moved around or handled very much before being set in an incubator.

And even if your egg did hatch, you shouldn't ever try to keep just one chicken - they are social birds and just one wouldn't thrive on its own. Also you'd have to have specialist rearing equipment ready, ie a proper heat lamp, brooder box, chick feeder and drinker and the correct food for young chicks. It's quite complex, hatching eggs and rearing chicks, and would be very expensive if you were trying to hatch very small numbers on just one occasion. If you really want to try this, maybe you could find out a lot more about it and then hire an incubator, get some eggs from a local poultry keeper, and take it form there. but remember, half the birds you hatch will be boys, and what are you going to do with them if nobody wants to give them a home?