When this happens, it's common to assume the hen is egg bound, but there is another reason for the "penguin" walk. She may have acites, which is a liver condition similar to cirrhosis of the liver in people. Fluid builds up in the abdominal cavity, and grows larger and heavier. It become almost impossible for the hen to walk.
Feel the bulge between her legs. Does it feel hard, or squishy like a water balloon? If it soft and squishy, it's probably acites, especially if it appears to be pushing her legs apart. Look at the other hens. Is the distance between your leghorn's legs farther apart than theirs? If so, she probably has acites and isn't egg bound.
But you can go ahead and place her in a warm bath for about half an hour, then leave her in a quiet place apart from the others, and she should lay the egg within a couple of hours if she's egg bound.
If not, and the fluid-filled sack keeps growing, you might want to ask about this on the emergencies and injuries forum.