The chance of breakeven is the estimate of the break even probability imbeded in the option price itself.  

Using the log-normal probability distribution assumption in the Black Scholes Merton model, it is possible to estimate the probability of the stock price falling above the break even value for an option investment. 

As an example, imagine a $25 strike call with a price of $1 and an implied volatility of 30% and a stock price of $20.  The break even price is $26, which represents the $25 strike price plus $1 option premium. 

Using the implied volatility of 30% and the current stock price, it is possible to estimate the likelihood that the stock price will be above $26 at expiration based on the log-normal probability assumption.  That probability is what is shown as the "chance of breakeven".