If two related plant species hybridise, their genomes are combined within a single nucleus, thereby forming an allotetraploid. How the emerging plant balances two co-evolved genomes is still a matter of ongoing research. Here, we focus on satellite DNA (satDNA), the fastest-turn over sequence class in eukaryotes, aiming to trace its emergence, amplification and loss during plant speciation and allopolyploidisation. As a model, we used Chenopodium quinoa Willd. (quinoa), an allopolyploid crop with 2n=4x=36 chromosomes. Quinoa originated by hybridisation of an unknown female American Chenopodium diploid (AA genome) with an unknown male Old World diploid species (BB genome), dating back 3.3 to 6.3 million years. Applying short read clustering to quinoa (AABB), C. pallidicaule (AA), and C. suecicum (BB) whole genome shotgun sequences, we classified their repetitive fractions, and identified and characterised seven satDNA families, together with the 5S rDNA model repeat. We show unequal satDNA amplification (two families) and exclusive occurrence (four families) in the AA- and BB-diploids by read mapping as well as Southern, genomic and fluorescent in situ hybridisation. As C. pallidicaule harbours a unique satDNA profile, we are able to exclude it as quinoa's parental species. Using quinoa long reads and scaffolds, we detected only limited evidence of interlocus homogenisation of satDNA after allopolyploidisation, but were able to exclude dispersal of 5S rRNA genes between subgenomes. Our results exemplify the complex route of tandem repeat evolution through Chenopodium speciation and allopolyploidisation, and may provide sequence targets for the identification of quinoa's progenitors.