A pigeon that falls down a chimney will often end up on the smoke shelf inside the chimney, that is there to prevent rain coming down the chimney from falling on the fire.
Please don't just leave it there, as it is trapped on your property then it is effectively under your control and to leave it to die slowly would be an offence under the Animal Welfare Act 2006
Pigeons can't fly back up the chimney vertically, they are too heavy, but they can fly down.
They fly towards light, so the first step would be to empty the fireplace and shine a light on it to tempt the pigeon down.
If the pigeon doesn't fly down, then it can be helped down by gently pushing it off the smoke shelf with a long pole or, if the bird is within sight, using a long reach grabber to remove it.
London Wildife Protection state that they always call the fire brigade as the fire service is obliged to remove anything that blocks the chimneys or ventilation systems. They quote this page as a reference source: http://www.legislation.gov.uk/uksi/2005/1541/contents/made
Once the bird is out of the chimney he will be a bit confused and slow so you can throw a towel over him to pick him up but please read the next paragraph before releasing it.
If the pigeon is trapped behind the gas fire then you have to call a Corgi registered fitter to move the fire. That is costly but needs to be done for health and safety reasons. As well as saving a life it prevents the house from smelling of rotting flesh for weeks on end.
Sometimes when a pigeon cannot be reached by any other means it will be necessary for a small hole to be made in the chimney to remove it, a bricklayer or builder would be the best person to do this.
If the bird has been up the chimney for some days please read Santa's Story for guidance on care and prognosis.