  We discuss a global anomaly associated with the coupling of chiral Weyl
fermions to gravity. The Standard Model based upon
$SU(3){\times}SU(2){\times}{U(1)}$ which has 15 fermions per generation is
shown to be inconsistent if all background spin manifolds with signature
invariant $\tau=8k$ are allowed. Similarly, GUTs based on odd number of Weyl
fermions are inconsistent. Consistency can be achieved by adding an extra Weyl
fermion which needs to couple only to gravity. For arbitrary $\tau$'s,
generalized spin structures are needed, and the global anomaly cancellation
requires that the net index of the total Dirac operator with spin and internal
gauge connections be even. As a result GUTs with fundamental multiplets which
contain multiples of 16 Weyls per generation are selected. The simplest
consistent GUT is the SO(10) model with a multiplet of 16 Weyls per generation.
The combined gravity and internal symmetry gauge group of the theory is then
$[Spin(3,1){\times}Spin(10)]/Z_2$. Physical implications of these results are
commented on.
