  Accretion onto the supermassive black hole in some active galactic nuclei
(AGN) drives relativistic jets of plasma, which dissipate a significant
fraction of their kinetic energy into gamma-ray radiation. The location of
energy dissipation in powerful extragalactic jets is currently unknown, with
implications for particle acceleration, jet formation, jet collimation, and
energy dissipation. Previous studies have been unable to constrain the location
between possibilities ranging from the sub-parsec-scale broad-line region to
the parsec-scale molecular torus, and beyond. Here we show using a simple
diagnostic that the more distant molecular torus is the dominant location for
powerful jets. This diagnostic, called the seed factor, is dependent only on
observable quantities, and is unique to the seed photon population at the
location of gamma-ray emission. Using $62$ multiwavelength, quasi-simultaneous
spectral energy distributions of gamma-ray quasars, we find a seed factor
distribution which peaks at a value corresponding to the molecular torus,
demonstrating that energy dissipation occurs $\sim 1$ parsec from the black
hole (or $\sim 10^{4}$ Schwarzchild radii for a $10^{9}M_{\odot}$ black hole).
