The Origin of Life Domain (OLD) is the period during which life on Earth began. Here, we derive and use a new phylogenetic algorithm to analyze Protein Families in order to reconstruct the chronological steps by which the OLD evolved. During this period, life began with the appearance of the fundamental components of life such as RNAs, DNAs, amino acids, and membranes. Chronologically, the Origin of Life preceded the Last Universal Common Ancestor, which then subsequently engendered modern life on Earth. Our phylogenetic algorithm allows us to explicitly answer previously unknown origin of life questions. Specifically, we explain and illustrate our computational methods by reconstructing the rings describing the evolution of the RNA and DNA worlds. We phylogenetically reconstruct how the RNA and DNA worlds evolved, infer the origins and chronological order of appearance of the first genetic codes, test whether the Ribosomal RNA world preceded the Membrane world, and interpret these new findings with respect to the experimental and theoretical origin of life studies by others.