  We prove the existence of a one-parameter family of pairwise non-isometric,
complete, positively curved, steady generalized Ricci solitons of gradient type
on $\mathbb{R}^3$ that are invariant under the natural cohomogeneity one action
of SO(3). In the context of generalized Ricci flow, this result represents the
analogue of Bryant's construction of the complete rotationally invariant steady
soliton for the Ricci flow.
