State files (having .lyc file extension) are used for saving the progress of a render when you need to close Chaotica and wish to resume rendering at a later point. They are saved via Tools > Save State.
Parameters (including imaging settings) are not contained within state files, so you must additionally save your parameters in .chaos format alongside the state file. You will need to have these parameters already loaded, with the resolution and supersampling settings matching those with which the state file was saved, before you attempt to load the state file.
State files can be very large if they are stored at high resolution, and especially with supersampling values greater than 2.