  We consider a system of three identical bosons in $\mathbb{R}^3$ with
two-body zero-range interactions and a three-body hard-core repulsion of a
given radius $a>0$. Using a quadratic form approach we prove that the
corresponding Hamiltonian is self-adjoint and bounded from below for any value
of $a$. In particular this means that the hard-core repulsion is sufficient to
prevent the fall to the center phenomenon found by Minlos and Faddeev in their
seminal work on the three-body problem in 1961. Furthermore, in the case of
infinite two-body scattering length, also known as unitary limit, we prove the
Efimov effect, \emph{i.e.}, we show that the Hamiltonian has an infinite
sequence of negative eigenvalues $E_n$ accumulating at zero and fulfilling the
asymptotic geometrical law $\;E_{n+1} / E_n \; \to \; e^{-\frac{2\pi}{s_0}}\,\;
\,\text{for} \,\; n\to +\infty$ holds, where $s_0\approx 1.00624$.
