  We study graviton-graviton scattering in partial-wave amplitudes after
unitarizing their Born terms. In order to apply S-matrix techniques, based on
unitarity and analyticity, we introduce an S-matrix associated to this
resummation that is free of infrared divergences. This is achieved by removing
the diverging phase factor calculated by Weinberg that multiplies the S matrix,
and that stems from the virtual infrared gravitons. A scalar graviton-graviton
resonance with vacuum quantum numbers (J^{PC}=0^{++}) is obtained as a pole in
the nonperturbative S-wave amplitude, which we call the {\it graviball}. Its
resonant effects along the physical real-s axis may peak at values
substantially lower than the UV cutoff squared of the theory. For some
scenarios, this phenomenon could have phenomenological consequences at
relatively low-energy scales, similarly to the \sigma resonance in QCD.
