How plants use the carbon they gain from photosynthesis remains a key area of study among plant ecologists. Although numerous theories have been presented throughout the years, the field lacks a clear null model. To fill this gap, I develop the first null model, or neutral theory, of plant carbon allocation using probability theory, plant biochemistry, and graph theory at the level of a leaf. Neutral theories have been used to establish a null hypothesis in molecular evolution and community assembly to describe how much of an ecological phenomenon can be described by chance alone. Here, the aim of a neutral theory of plant carbon allocation is to ask: how is carbon partitioned between sinks if one assumes plants do not prioritize certain sinks over others? Using the biochemical network of plant carbon metabolism, I show that if allocation was strictly random, carbon is more likely to be allocated to storage, defense, respiration, and finally growth. This ‘neutral hierarchy’ suggests that a sink’s biochemical distance from photosynthesis plays an important role in carbon allocation patterns, highlighting the potentially adaptive role of this biochemical network for plant survival in variable environments. A brief simulation underscores that our ability to measure the carbon allocation from photosynthesis to a given sink is unreliable due to simple probabilistic rules. While neutral theory may not explain all patterns of carbon allocation, its utility is in the minimal assumptions and role as a null model against which future data should be tested against.