Several solutions have been presented here, but I'll offer my take on this. The answer is no. There is no alternative to the chain/derailleur combo that would offer all of the benefits of a chain/derailleur combo.
Shaft drive, belt drive, internally geared hub, all of them suffer from the same fundamental problem: fixing a flat rear tire is difficult on those.
At least on an internally geared hub, all of them must have some lever against the frame to provide a point of torque, as the hub must be able to convert low torque (and high speed) to high torque (and low speed) or vice versa. The requirement to disconnect and re-connect the torque lever adds to the complexity of fixing a rear tire flat.
Similarly, internally geared hubs must have horizontal dropouts, to be able to adjust chain tension. Adjusting the chain tension on horizontal dropouts is time-consuming. You don't want that to complicate your flat fixing. Also, wrapping the chain around the sprocket is time-consuming. On a derailleur system, you just bend the rear derailleur a little and push the rear wheel in.
Not only that, but what do you do if a chain link breaks? On a derailleur system, you just make the chain a bit shorter using a portable chain tool you carry with you in your emergency toolbox (using a special pin, if using a Shimano chain -- the special pins are so lightweight you can carry several with you).
Also, what if the internally geared hub breaks? Everything on a derailleur is able to be temporarily fixed with just allen keys, chain tool, etc. Even if the chain tensioner breaks, you just select what gear you want and use the bike as a single-speed bike for the rest of the journey. If front or rear derailleur breaks, you use the remaining one that is still functional.
What if one of the only two sprockets (one front, one rear) on an internally geared hub breaks? On a derailleur system, you have at least two sprockets on the front and multiple on the rear. You can use one of the remaining sprockets. On an internally geared bike, you don't have any option.
I don't think any other solution allows the easy temporary workarounds possible on a derailleur system, the easiness of fixing a rear tire flat, the ability to make the chain a link shorter in case a chain link breaks, etc. About the only problem a derailleur system doesn't solve is a freewheel failure. Usually, freewheels give an early warning before completely failing.