New Chance for a New Start in Life Act of 2014 - Directs the Secretary of Labor, subject to the availability of appropriations, to make grants to state and local governments and Indian tribes to carry out employment training programs to assist long-term unemployed persons obtain the skills and training to reenter the workforce and fill jobs in sectors of the economy projected to have the highest rates of demand during the period 2012 through 2022.

Prescribes certain grant condition and use requirements.

Declares that an individual receiving services or compensation funded by a grant under this Act shall not be cause for any reduction in the amount of unemployment compensation that individual is otherwise due.