The BlockChain Neural Network increments gradually neurons as user information or data increases, offering a biologically inspired "Neuron as a Service" (NaaS) solution. The additional neurons codify both the new information to be added to the "neural block" and the previous neurons potential to form the "neural chain". This configuration provides the proposed algorithm with the same properties found in the BlockChain: security and decentralization with the same validation process: mining the input neurons until the neural network solution is found. The mathematical model of the Neural Networks in BlockChain configuration is presented in this paper with evidences of its stable learning convergence during its learning process. The main advantage of this research proposal is the biological simplicity of the solution, however it suffers high computational cost when the number of neurons increase. Experimental results that validate the proposed method are presented with optimistic conclusions; this paper provides the biologically inspired mathematical model as a digital step forward to avoid physical currencies, documentation and contracts.