Chocolate layer cake tears easily
As cascabel mentions, it sounds like the bottom layer may be domed - if so, that uneven surface can encourage splitting by having uneven tension along the bottom.

One possible remedy, then, is to level the bottom cake.  you'll end up with scraps, from cutting to smooth the cake top, but it should help keep the level from splitting and sliding.

Another possible remedy is, flipping the bottom cake over before stacking the upper layer.  This will give a smooth top, and the pressure should even out the rounded bottom without need for cutting.  I've only heard of this, not tried it, so I can't say for sure it will work - but it was mentioned as a possibility for a for soft tender cake, which this is (I can see it not working for a denser or sturdier baked good).

One outside possibility... you might try cooling the cake before stacking.  Hot, or even warm, cake tends to be more fragile, and warmer icing more slidy.  If you are already waiting until the cake is fully cool before trying to stack, you might try going even further and chilling in the fridge (or even freezing) before assembly with the idea it can come up to temperature before serving - it'll be more likely to stay put warming up when already stably affixed, under the theory an object at rest likes to stay at rest :)