I see two questions in this. First, YES it is legal for you to eat what you slaughter and process yourself. Second, it may or may not be legal to slaughter a chicken on your own property where you live. You can either check your town, county, and state regulations to find out, or you can just do it quietly when nobody is looking. There aren't any dangerous by-products of slaughtering, so just don't subject your neighbors to the sight of it, and dispose of the parts you don't want in a sanitary manner. That should take care of the issue no matter what your area's requirements are.