  We present new constraints on the spectral index n_T of tensor fluctuations
from the recent data obtained by the BICEP2 experiment. We found that the
BICEP2 data alone slightly prefers a positive, "blue", spectral index with
n_T=1.36\pm0.83 at 68 % c.l.. However, when a TT prior on the tensor amplitude
coming from temperature anisotropy measurements is assumed we get
n_T=1.67\pm0.53 at 68 % c.l., ruling out a scale invariant $n_T=0$ spectrum at
more than three standard deviations. These results are at odds with current
bounds on the tensor spectral index coming from pulsar timing, Big Bang
Nucleosynthesis, and direct measurements from the LIGO experiment. Considering
only the possibility of a "red", n_T<0 spectral index we obtain the lower limit
n_T > -0.76 at 68 % c.l. (n_T>-0.09 when a TT prior is included).
