This is the author accepted manuscript. The final version is available from APS via http://dx.doi.org/10.1103/PhysRevLett.114.157004 ; We use first-principles calculations to study structural, vibrational, and superconducting properties of (H_2)S at pressures P?200??GPa. The inclusion of zero-point energy leads to two different possible dissociations of (H_2)S, namely 3(H_2)S?2(H_3)S+S and 5(H_2)S?3(H_3)S+HS_2, where both (H_3)S and HS_2 are metallic. For (H_3)S, we perform nonperturbative calculations of anharmonic effects within the self-consistent harmonic approximation and show that the harmonic approximation strongly overestimates the electron-phonon interaction (??2.64 at 200 GPa) and T_c. Anharmonicity hardens H?S bond-stretching modes and softens H?S bond-bending modes. As a result, the electron-phonon coupling is suppressed by 30% (??1.84 at 200 GPa). Moreover, while at the harmonic level T_c decreases with increasing pressure, the inclusion of anharmonicity leads to a T_c that is almost independent of pressure. High-pressure hydrogen sulfide is a strongly anharmonic superconductor. ; We acknowledge discussions with I.?I. Mazin and support from the Agence Nationale de la Recherche, Grant No. ANR-13-IS10-0003-01. Computer facilities were provided by PRACE, CINES, CCRT, and IDRIS. I.?E. acknowledges financial support from the Department of Education, Language Policy, and Culture of the Basque Government (Grant No. BFI-2011-65) and the Spanish Ministry of Economy and Competitiveness (FIS2013-48286-C2-2-P). C.?J.?P. and R.?J.?N. thank EPSRC (UK) for financial support. J.?R.?N. acknowledges financial support from the Cambridge Commonwealth Trust. Y. Li thanks the National Natural Science Foundation of China for support under Grants No. 11204111 and No. 11404148. Y. Zhang and Y. Ma thank the Natural Science Foundation of China for support under Grant No. 11274136 and the 2012 Changjiang Scholars Program of China.