Elucidating the appropriate microscopic degrees of freedom within neutron stars remains an open question which impacts nuclear physics, particle physics and astrophysics. The recent discovery of the first non-trivial dibaryon, the d∗(2380), provides a new candidate for an exotic degree of freedom in the nuclear equation of state at high matter densities. In this paper a first calculation of the role of the d∗(2380) in neutron stars is performed, based on a relativistic mean field description of the nucleonic degrees of freedom supplemented by a free boson gas of d∗(2380). The calculations indicate that the d∗(2380) would appear at densities around three times normal nuclear matter saturation density, influencing the upper mass limit for a stable neutron star and the neutron and proton fractions. New possibilities for neutron star cooling mechanisms arising from the d∗(2380)are also predicted