  We present a criterion that provides an easy sufficient condition in order
that a collection of Abelian integrals has the Chebyshev property. This
condition involves the functions in the integrand of the Abelian integrals and
can be checked, in many cases, in a purely algebraic way. By using this
criterion, several known results are obtained in a shorter way and some new
results, which could not be tackled by the known standard methods, can also be
deduced.
