The so-called stripe phase of the manganites is an important example of the complex behaviour of metal oxides, and has long been interpreted as the localisation of charge at atomic sites. Here, we demonstrate via resistance measurements on La_0.50Ca_0.50MnO₃ that this state is in fact a prototypical charge density wave (CDW) which undergoes collective transport. Dramatic resistance hysteresis effects and broadband noise properties are observed, both of which are typical of sliding CDW systems. Moreover, the high levels of disorder typical of manganites result in behaviour similar to that of well-known disordered CDW materials. Our discovery that the manganite superstructure is a CDW shows that unusual transport and structural properties do not require exotic physics, but can emerge when a well-understood phase (the CDW) coexists with disorder.