  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 $R_{J}$.
