Covering: up to 2020 What was first? Coenzymes or proteins? These questions are archetypal examples of causal circularity in living systems. Classically, this "chicken-and-egg"problem was discussed for the macromolecules RNA, DNA and proteins. This report focuses on coenzymes and cofactors and discusses the coenzyme/protein pair as another example of causal circularity in life. Reflections on the origin of life and hypotheses on possible prebiotic worlds led to the current notion that RNA was the first macromolecule, long before functional proteins and hence DNA. So these causal circularities of living systems were solved by a time travel into the past. To tackle the "chicken-and-egg"problem of the protein-coenzyme pair, this report addresses this problem by looking for clues (a) in the first hypothetical biotic life forms such as protoviroids and the last unified common ancestor (LUCA) and (b) in considerations and evidence of the possible prebiotic production of amino acids and coenzymes before life arose. According to these considerations, coenzymes and cofactors can be regarded as very old molecular players in the origin and evolution of life, and at least some of them developed independently of α-amino acids, which here are evolutionarily synonymous with proteins. Discussions on "chicken-and-egg"problems open further doors to the understanding of evolution.