  We construct the effective field theory for a single massive higher-spin
particle in flat spacetime. Positivity bounds of the S-matrix force the cutoff
of the theory to be well below the naive strong-coupling scale, forbid any
potential and make therefore higher-derivative operators important even at low
energy. As interesting application, we discuss in detail the massive spin-3
theory and show that an extended Galileon-like symmetry of the longitudinal
modes, even with spin, emerges at high energy.
