Up until around the age of 12 this is a common phrase in every child's vocabulary. Used to question the validity of somebody's statement. In cambridgeshire there were two variations of chinny reckon or "Chinny Rah-Kon". Firstly one would put their tongue imbetween their bottom teeth and lip, making it swell, and make a low noise before saying "Chinny Reckon" or "Itchy Chin". The phrase "Chin Spin" was also used in the same context.
"I've scored twenty five goals on the playground this week"
"Yeah, Chinny Reckon"