Recent µSR measurements for SrPtAs revealed time-reversal-symmetry breaking with the onset of superconductivity suggesting an unconventional superconducting state. We investigate this possibility via functional renormalization group and find a (chiral) d + id order parameter favored by the multi-band fermiology and hexagonal symmetry of SrPtAs. The d + id gap exhibits significant gap anisotropies as well as gap differences on the different bands and only has point nodes at the Brillouin zone corners. The lack of extended nodes and the spontaneously broken time-reversal symmetry of the d + id state are in agreement with the µSR experiments. Our results, together with the experimental evidence, thus suggests that SrPtAs might be the first known instance of chiral d-wave superconductivity.