IUPAC defines chain propagation as a reaction of an active center on the growing polymer molecule, which adds one monomer molecule to form a new polymer molecule (RM°) one repeat unit longer. 
For radical polymerization, the active center remains an atom with an unpaired electron.  The addition of the second monomer and a typical later addition step are
* RM° + M → RM°
* RM° + M → RM°
For some polymers, chains of over 1000 monomer units can be formed in milliseconds.