  Majorana fermion (MF) excitations in solid state system have non-Abelian
statistics which is essential for topological quantum computation. Previous
proposals to realize MF, however, generally requires fine-tuning of parameters.
Here we explore a platform which avoids the fine-tuning problem, namely a
ferromagnetic chain deposited on the surface of a spin-orbit coupled $s$-wave
superconductor. We show that it generically supports zero-energy topological MF
excitations near the two ends of the chain with minimal fine-tuning. Depending
on the strength of the ferromagnetic moment in the chain, the number of MFs at
each end, $n$, can be either one or two, and should be revealed by a robust
zero-bias peak (ZBP) of height $2ne^2/h$ in scanning tunneling microscopy (STM)
measurements which would show strong (weak) signals at the ends (middle) of the
chain. The role of an approximate chiral symmetry which gives an integer
topological invariant to the system is discussed.
