  We report detailed $^{75}$As-NQR investigations of the locally
non-centrosymmetric superconductor SrPtAs. The spin-lattice relaxation studies
prove weakly coupled multi-gap superconductivity. The Hebel-Slichter peak, a
hallmark of conventional superconductivity, is strongly suppressed, which
points to an unconventional superconducting state. The observed behavior
excludes a superconducting order parameter with line nodes and is consistent
with proposed $f$-wave and chiral $d$-wave order parameters.
