  Recent $\mu$SR measurements on SrPtAs revealed time-reversal-symmetry
breaking with the onset of superconductivity [Biswas et al., Phys. Rev. B 87,
180503(R) (2013)], suggesting an unconventional superconducting state. We
investigate this possibility via functional renormalization group and find a
chiral $(d+\mathrm{i}d)$-wave order parameter favored by the multiband
fermiology and hexagonal symmetry of SrPtAs. This $(d+\mathrm{i}d)$-wave state
exhibits significant gap anisotropies as well as gap differences on the
different bands, but only has point nodes on one of the bands at the Brillouin
zone corners. We study the topological characteristics of this superconducting
phase, which features Majorana-Weyl nodes in the bulk, protected surface
states, and an associated thermal Hall response. The lack of extended nodes and
the spontaneously broken time-reversal symmetry of the $(d+\mathrm{i}d)$-wave
state are in agreement with the $\mu$SR experiments. Our theoretical findings
together with the experimental evidence thus suggests that SrPtAs is the first
example of chiral $d$-wave superconductivity.
