This means 'yeah right' or 'I don't beleive you'. It is pronounced 'chinny re-kon' and has more impact if you say it whilst stroking your chin. We used to say it at primary school, but it might just be a Northern thing!
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.
Chinny beard (noun) /tʃɪnny bɪəd/
A phrase to exclaim when it is suspected someone is lying or exaggerating, originating from the dubious rubbing of the chin. Perhaps a solely Peterborough term.