The diversity and complexity of the human brain are widely assumed to be encoded within a constant genome. Somatic gene recombination, which changes germline DNA sequences to increase molecular diversity, could theoretically alter this code but has not been documented in the brain, to our knowledge. Here we describe recombination of the Alzheimer's disease-related gene APP, which encodes amyloid precursor protein, in human neurons, occurring mosaically as thousands of variant `genomic cDNAs' (gencDNAs). gencDNAs lacked introns and ranged from full-length cDNA copies of expressed, brain-specific RNA splice variants to myriad smaller forms that contained intra-exonic junctions, insertions, deletions, and/or single nucleotide variations. DNA in situ hybridization identified gencDNAs within single neurons that were distinct from wild-type loci and absent from non-neuronal cells. Mechanistic studies supported neuronal `retro-insertion' of RNA to produce gencDNAs; this process involved transcription, DNA breaks, reverse transcriptase activity, and age. Neurons from individuals with sporadic Alzheimer's disease showed increased gencDNA diversity, including eleven mutations known to be associated with familial Alzheimer's disease that were absent from healthy neurons. Neuronal gene recombination may allow `recording' of neural activity for selective `playback' of preferred gene variants whose expression bypasses splicing; this has implications for cellular diversity, learning and memory, plasticity, and diseases of the human brain.