Massachusetts General Law Chapter 40B is a state law pertaining to local and regional affordable housing development.  The reference to "40B" in affordable housing projects is regarding proposed residential development in communities that have not achieved 10% of overall housing stock. 

Each community in Massachusetts is required to have a minimum 10% of its housing inventory be considered as affordable (generally 80% median household income). If a community has not achieved 10% affordable threshold, it is subject to a Zoning Board of Appeals review process known as a Comprehensive Permit allowing exceptions from zoning for dimensional, density, and parking requirements.