How could a mutation to an amino acid chain cause no change to a cell's structure or function?

I asume you mean the to one of the codons that specify amino acids? if so the answer is redundancy

Explanation:

Because there are only 20 different amino acids but 64 possible codons, most amino acids are indicated by more than one codon. A phenomenon known as redundancy or degeneracy, and it is important to the genetic code because it minimizes the harmful effects that incorrectly placed nucleotides can have on protein synthesis.

Answer: Different codons code for the same amino acids.

Explanation: Some amino acids can have multiple codons that code for them. If a mutation changes a codon to another one that codes for the same amino acid, there will be no change to the proteins it makes.