I’ve done a little bit of research, and yes! You can grow chickpeas. I found this really useful document online, click here, provided by Sewing New Seeds. It tells you exactly what to do and the possible problems and diseases associated with growing chickpeas. Obviously I’ve not tried this myself yet, but I am definitely going to give it some thought with a view to possibly growing some next year.
I have found a website where you can buy chickpea seeds from called The Organic Gardening Catalogue, just in case you would like to have a go too.