Mankind's productive use of the low Earth orbit (LEO), from 400-2,000km in altitude, is at risk from increasing counts of debris objects and derelict satellites, which pose collision risks to active spacecraft. Of particular concern to space agencies and industry is the Kessler Syndrome (KS), which is the term for a hypothetical collapse scenario in which collisions between debris and satellites cause more debris, causing a destructive cascade that leaves the orbital environment unusable. In order to better understand this KS tipping point, the KESSYM model has been developed as a stochastic simulation of all the objects in the LEO. This model provides a forecast for the evolution of the orbital environment into the future, including the expected year, if any, that the KS collapse occurs. KESSYM allows for certain risks, such as war or terrorism in space, solar flares, or unconstrained exploitation of the space resources to be analyzed alongside KS mitigation measures, such as the hardening of spacecraft against debris, avoidance of collisions, removal of debris, and effective regulation. The conclusions drawn from the KESSYM simulation are that the KS is almost an inevitability within 200-250 years of today's date, but can be delayed or avoided altogether if action is taken.