  The heavy fermion superconductor URu$_2$Si$_2$ is a candidate for chiral,
time-reversal symmetry-breaking superconductivity with a nodal gap structure.
Here, we microscopically visualized superconductivity and spatially
inhomogeneous ferromagnetism in URu$_2$Si$_2$. We observed linear-$T$
superfluid density, consistent with d-wave pairing symmetries including chiral
d-wave, but did not observe the spontaneous magnetization expected for chiral
d-wave. Local vortex pinning potentials had either four- or two-fold rotational
symmetries with various orientations at different locations. Taken together,
these data support a nodal gap structure in URu$_2$Si$_2$ and suggest that
chirality either is not present or does not lead to detectable spontaneous
magnetization.
