The first amino acid of any polypeptide chain in eukaryotes is

The correct option is methionine.

During the process of translation (protein synthesis) in eukaryotic organisms, the genetic code on the messenger RNA (mRNA) is translated into a sequence of amino acids to form a polypeptide chain.

Translation initiation begins at a specific start codon on the mRNA molecule. In eukaryotes, the universal start codon is AUG.
This codon specifically codes for the amino acid methionine.

A specialized initiator transfer RNA (tRNA), designated as Met-tRNA_i^Met, recognizes the AUG start codon and binds to the ribosomal initiation complex.
Consequently, methionine is positioned as the very first amino acid at the amino-terminal (N-terminal) end of the nascent polypeptide chain, even though it may be enzymatically modified or cleaved off in subsequent post-translational modification steps.