We study a dynamical mechanism that generates a composite vectorlike fermion, formed by the binding of an $N$-tuplet of elementary chiral fermions to an $N$-tuplet of scalars. Deriving the properties of the composite fermion in the large $N$ limit, we show that its mass is much smaller than the compositeness scale when the binding coupling is near a critical value. We compute the contact interactions involving four composite fermions, and find that their coefficients scale as $1/N$. Physics beyond the Standard Model may include composite vectorlike fermions arising from this mechanism.