Even if the chain doesn't break on you (and I've definitely broken chains before) your braking power is still completely compromised lacking a front brake. The rear wheel simply doesn't have enough traction while braking to stop you quickly. The harder you break the more your weight shifts to the front wheel. It doesn't take much to simply lock up the rear wheel and skid. In fact that's a popular little competitive event for fixed gear riders. They'll lock the rear wheel and see how far they can skid before they finally come to a stop. They're deliberately unweighting the rear wheel as much as possible but the point being is that the braking offered by rear wheel only is poor at best.