  We present an effective field theory (EFT) at leading order to describe light
single-$\Lambda$ hypernuclei. Owing to the weak $\Lambda$ binding and to the
$\Lambda N$ short interaction range, meson exchange forces are approximated by
contact interactions within a pionless EFT where the only degrees of freedom
are baryons. At leading order, the $\Lambda$-nuclear interaction contains two
2-body (singlet and triplet) and three 3-body interaction terms, a total of 5
terms associated with 5 coupling strengths or low energy constants (LECs). We
adopt the 2-body LECs from hyperon-nucleon scattering data and interaction
models that constrain the $\Lambda N$ scattering lengths, while the 3-body LECs
are adjusted using both 3-body and 4-body hypernuclear binding energies. To
calculate the binding energies for A-body systems with A$>$2, we expand the
wavefunctions using a correlated Gaussian basis. The stochastic variational
method is employed to select the non-linear parameters. The resulting
\nopieft~is then applied to calculate the $\Lambda$ separation energy in
$_\Lambda^5$He, where the adjusted 3-body interactions largely resolve the
known overbinding problem of $_\Lambda^5$He.
