Google have announced they will no longer support Chrome running on Mac OS 10.8 and below. Chrome will continue to function on these systems, but no new updates will be released. From a security point of view, it would make sense where possible to update your system to Mac OS 10.9 or later. Please bear in mind that updating from a system such as 10.6 to 10.11  may affect the performance of applications, so please check the compatibility of any important software before upgrading. It may also require hardware upgrades to run the newer system.