Tenants' Right to Organize Act This bill provides for the right of tenants who receive certain rental assistance to establish, operate, and participate in a tenant organization. Specifically, tenants who participate in Housing Choice Voucher (i.e., Section 8 tenant-based housing assistance) or Low-Income Housing Tax Credit programs administered by the Department of Housing and Urban Development have the right to engage in a tenant organization to address issues related to their living environment and participate in community development activities. Public housing agencies and unit owners are required to recognize tenant organizations and allow tenants to conduct protected activities, including distributing leaflets, initiating tenant contact, and convening meetings in the building. A public housing agency or building owner may not require prior permission for any of these activities. Further, these entities may not retaliate against a tenant for participating in a tenant organization. The bill also provides grants for state and local organizations for training and outreach with respect to tenant organization capacity building and technical assistance.