  Spanning a broad range of physical systems, complex symmetry breaking is
widely recognized as a hallmark of competing interactions. This is exemplified
in superfluid $^3$He which has multiple thermodynamic phases with spin and
orbital quantum numbers $S=1$ and $L=1$, that emerge on cooling from a nearly
ferromagnetic Fermi liquid. The heavy fermion compound UPt$_3$ exhibits similar
behavior clearly manifest in its multiple superconducting phases. However,
consensus as to its order parameter symmetry has remained elusive. Our small
angle neutron scattering measurements indicate a linear temperature dependence
of the London penetration depth characteristic of nodal structure of the order
parameter. Our theoretical analysis is consistent with assignment of its
symmetry $L=3$ odd parity state for which one of the three thermodynamic phases
in non-zero magnetic field is chiral.
