While the previous paragraph describes theories of how LENR might occur in present day experiments, it's based on a set of actual observations made in the 1940s and 50s, (picture 1). In 1958, Luis Alvarez in a report to the Unitied Nations[8 open access] on high energy physics announced that his team had observed several muon catalyzed fusion events. A muon is a naturally occurring particle that is a member of the same family of particles,(leptons), as the electron. The muon has the same charge as an electron, but it is about 200 times more massive. As a consequence of this extra mass, the hypothesis described above for heavy electrons actually takes place. Interestingly, it was reported in the proceedings of a liquid scintillation conference that as far back as 1958, the term cold fusion was being reported by the press and even then creating a fair bit of mayhem.
You may have heard how Canadian uranium stocks fell several months ago when a newspaper carried the announcement that uranium was now unnecessary because of the discovery of 'cold fusion'.Jackson, of Jackson EM book fame, did an analysis of the process in 1957 and writing in the +American Physical Society's Physical Review determined that in all likelihood, without a much cheaper source of muons, it would be impossible to derive any useful power,(picture 2). For more detail on Jackson's involvement and a rather complete explanation of the subject in general, check out Wikipedia.
Alvarez and Jackson both mention that similar observations had been made as early as 1947.
1. Frank on hypothetical muon fusion
FRANK F.C. (1947). Hypothetical Alternative Energy Sources for the ‘Second Meson’ Events, Nature, 160 (4068) 525-527. DOI: 10.1038/160525a0
2. Experimental observation I
LATTES C.M.G., OCCHIALINI G.P.S. & POWELL C.F. (1947). Observations on the Tracks of Slow Mesons in Photographic Emulsions, Nature, 160 (4066) 453-456. DOI: 10.1038/160453a0
3. Jackon on Muon Fusion with speculations on useful energy release
Jackson J. (1957). Catalysis of Nuclear Reactions between Hydrogen Isotopes by μ- Mesons, Physical Review, 106 (2) 330-339. DOI: 10.1103/PhysRev.106.330
4. Wheeler on muon fusion
Wheeler J. (1949). Some Consequences of the Electromagnetic Interaction between μ--Mesons and Nuclei, Reviews of Modern Physics, 21 (1) 133-143. DOI: 10.1103/RevModPhys.21.133
5. Cold fusion report circa 1958 (open access)
6. Alvarez in Physical Review on Muon Fusion
Alvarez L., Bradner H., Crawford F., Crawford J., Falk-Vairant P., Good M., Gow J., Rosenfeld A., Solmitz F. & Stevenson M. & (1957). Catalysis of Nuclear Reactions by μ Mesons, Physical Review, 105 (3) 1127-1128. DOI: 10.1103/PhysRev.105.1127
7. Very handy Wikipedia article on muon catalyzed fusion
8. Alvarez to the United Nations (open access)