@KristianHarstad All birds are equally related to _T. rex_, since they're all descended from a common ancestor that split off from the lineage that would lead to tyrannosaurs at the same time, sometime in the early Jurassic. It's vaguely possible that out of all modern birds, chickens have the genome most like that of the last common ancestor of birds and tyrannosaurs ... but it seems really, really unlikely.

The paleognaths—tinamous, kiwis, and large ratites such as ostriches and emus—are anatomically more like ancestral birds than are neognaths such as chickens. Most likely they're more genetically similar as well.