Stop codons

Do stop codons only occur at the end of mRNA molecules, since each mRNA codes for a single polypeptide chain?

Not necessarily. On a basic level, you can think of it as that way, but practically, stop codons need not be present where the mRNA ends, since during transcription, their DNA complements do not code for any stoppage of the transcription process.

Oh wait that's not quite what I meant...

mRNA copies all of the DNA and some bits of DNA happen to code for a stop codon in mRNA, so wen translation occurs there is no complementary triplet on tRNA so translation ends.