We present a first internal delensing of CMB maps, both in temperature and polarization, using the public foreground-cleaned (SMICA) Planck 2015 maps. After forming quadratic estimates of the lensing potential, we use the corresponding displacement field to undo the lensing on the same data. We build differences of the delensed spectra to the original data spectra specifically to look for delensing signatures. After taking into account reconstruction noise biases in the delensed spectra, we find an expected sharpening of the power spectrum acoustic peaks with a delensing efficiency of 29 % (TT) 25 % (TE) and 22 % (EE). The detection significance of the delensing effects is very high in all spectra: 12 σ in EE polarization; 18 σ in TE; and 20 σ in TT. The null hypothesis of no lensing in the maps is rejected at 26 σ. While direct detection of the power in lensing B-modes themselves is not possible at high significance at Planck noise levels, we do detect (at 4.5 σ {under the null hypothesis}) delensing effects in the B-mode map, with 7 % reduction in lensing power. Our results provide a first demonstration of polarization delensing, and generally of internal CMB delensing, and stand in agreement with the baseline ΛCDM Planck 2015 cosmology expectations.