There has been some work in this area but with three chat bots. Xing Han Lu has developed some code called Generative Adversarial Bots (GABs) which builds on the concept of Generative Adversarial Networks invented by Ian Goodfellow. See his pioneering paper "Generative Adversarial Networks".
There is a very brief Google presentation here.
The basic idea of GABs is to "compare the performance and human-likeness of conversational chatbots by generating conversation between two bots, and evaluating the response using Turing Tests". "Generative Adversarial Bots (GABs) are bots that are pitched up against each other, and generate a conversation that is used to train a third bot".
You might want to also check out "Adversarial Learning for Neural Dialogue Generation" by Jiwei Li, Will Monroe, Tianlin Shi, Sébastien Jean, Alan Ritter and Dan Jurafsky. From their abstract:
In this paper, drawing intuition from the Turing test, we propose using adversarial training for open-domain dialogue generation: the system is trained to produce sequences that are indistinguishable from human-generated dialogue utterances. We cast the task as a reinforcement learning (RL) problem where we jointly train two systems, a generative model to produce response sequences, and a discriminator---analagous to the human evaluator in the Turing test--- to distinguish between the human-generated dialogues and the machine-generated ones. The outputs from the discriminator are then used as rewards for the generative model, pushing the system to generate dialogues that mostly resemble human dialogues.
Jiwei Li, one of the authors, has posted the code here.