Studies of solar-type binaries have found coplanarity between the equatorial and orbital planes of systems with < 40 AU separation . By comparison , the alignment of the equatorial and orbital axes in the substellar regime , and the associated implications for formation theory , are relatively poorly constrained . Here we present the discovery of the rotation period of 3.32 \pm 0.15 hours from 2MASS J0746+20A - the primary component of a tight ( 2.7 AU ) ultracool dwarf binary system ( L0+L1.5 ) . The newly discovered period , together with the established period via radio observations of the other component , and the well constrained orbital parameters and rotational velocity measurements , allow us to infer alignment of the equatorial planes of both components with the orbital plane of the system to within 10 degrees . This result suggests that solar-type binary formation mechanisms may extend down into the brown dwarf mass range , and we consider a number of formation theories that may be applicable in this case . This is the first such observational result in the very low mass binary regime . In addition , the detected period of 3.32 \pm 0.15 hours implies that the reported radio period of 2.07 \pm 0.002 hours is associated with the secondary star , not the primary , as was previously claimed . This in turn refutes the claimed radius of 0.78 \pm 0.1 R _ { J } for 2MASS J0746+20A , which we demonstrate to be 0.99 \pm 0.03 R _ { J } .