The E1 and E2 envelope proteins of hepatitis C virus (HCV) form a heterodimer that drives virus-host membrane fusion. Here, we analyze the role of each amino acid in E1E2 function, expressing 545 individual alanine mutants of E1E2 in human cells, incorporating them into infectious viral pseudoparticles, and testing them against 37 different monoclonal antibodies (MAbs) to ascertain full-length translation, folding, heterodimer assembly, CD81 binding, viral pseudoparticle incorporation, and infectivity. We propose a model describing the role of each critical residue in E1E2 functionality and use it to examine how MAbs neutralize infection by exploiting functionally critical sites of vulnerability on E1E2. Our results suggest that E1E2 is a surprisingly fragile protein complex where even a single alanine mutation at 92% of positions disrupts its function. The amino-acid-level targets identified are highly conserved and functionally critical and can be exploited for improved therapies and vaccines.