  We apply a recently proposed covariant power counting in nucleon-nucleon
interactions to study strangeness $S=-1$ $\Lambda N-\Sigma N$ interactions in
chiral effective field theory. At leading order, Lorentz invariance introduces
12 low energy constants, in contrast to the heavy baryon approach, where only
five appear. The Kadyshevsky equation is adopted to resum the potential in
order to account for the non-perturbative nature of hyperon-nucleon
interactions. A fit to the $36$ hyperon-nucleon scattering data points yields
$\chi^2\simeq 16$, which is comparable with the sophisticated phenomenological
models and the next-to-leading order heavy baryon approach. However, one cannot
achieve a simultaneous description of the nucleon-nucleon phase shifts and
strangeness $S=-1$ hyperon-nucleon scattering data at leading order.
