Hi, Pete:
Tool sharpness is usually the obvious suspect when we are not getting the results we want, but in this case if the tool is sharp enough to produce an acceptable cut on the rest of the blank then it may be something else.
Some wood species are just naturally brittle and will chip out at the edges much worse than others. Purpleheart springs to mind as an example of that.
Tool presentation and cutting direction might be another factor. If the bowl corners are upturned so that the corners are the highest point of the turning then you cut the sides of the bowl just the same as if the bowl were fully round, from the base to the rim with the bevel rubbing and trying for a shearing cut. The tricky bit comes when you get to the area where the cut becomes interrupted. You have to continue to maintain the same tool orientation and edge presentation while moving the gouge along your chosen cut line even though it is no longer fully supported by the wood. Personally, I find this easier to do using a bowl gouge with the traditional grind rather than a side ground gouge, but that may just be because I am more used to that grind. This pic shows the direction of my cut if nothing else:
If your wings are horizontal so that the edge running from one corner to the next is a straight line, like this:
then you might have better luck cutting in from the corners to the bowl side as opposed to out from the bowl side to the corner. Just like the initial levelling cuts across the face of a newly mounted blank you should be able get an acceptable surface cutting in either direction, but the amount of chip out at the edge might be different depending on which way you are cutting.
If the wings are downturned as in the bowl photos Chris and Dean posted, or more extremely in this bowl:
then the area between the bowl wall and the downturned corners is a cove and, just like when spindle turning, you should make your cuts from both sides to meet in the middle. The cut on the underside of the corners is the same cut you make when hollowing the interior of a bowl and should be made in the same direction.
If all else fails and you still have some minor chipping along the edges you can clean it up with a block plane, spokeshave, or even a belt sander like this:
Good Luck!
Bob
