We present the results of an investigation into the atomic structure and magnetism of 2 nm diameter Co nanoparticles embedded in an antiferromagnetic Cr matrix. The nanocomposite films used in this study were prepared by co-deposition directly from the gas phase, using a gas aggregation source for the Co nanoparticles and a molecular beam epitaxy (MBE) source for the Cr matrix material. Co K and Cr K edge extended x-ray absorption fine structure (EXAFS) experiments were performed in order to investigate atomic structure in the embedded nanoparticles and matrix respectively, while magnetism was investigated by means of a vibrating sample magnetometer. The atomic structure type of the Co nanoparticles is the same as that of the Cr matrix (b.c.c.) although with a degree of disorder. The net Co moment per atom in the Co/Cr nanocomposite films is significantly reduced from the value for bulk Co, and decreases as the proportion of Co nanoparticles in the film is decreased; for the sample with the most dilute concentration of Co nanoparticles (4.9% by volume), the net Co moment was 0.25 /atom. After field cooling to below 30 K all samples showed an exchange bias, which was largest for the most dilute sample. Both the structural and magnetic results point towards a degree of alloying at the nanoparticle/matrix interface, leading to a core/shell structure in the embedded nanoparticles consisting of an antiferromagnetic CoCr alloy shell surrounding a reduced ferromagnetic Co core.