The purpose of this research study is to find out whether the drug mexiletine will be effective in lowering motor neuron electrical activity in the brains and nerves in the arms of people with ALS. The investigators will also determine if there are any signs that the drug may slow down the progression of ALS and reduce muscle cramps and muscle twitching. This will be determined through transcranial magnetic stimulation (TMS) and threshold tracking nerve conduction studies (TTNCS). In this trial, the participants will be taking either 300mg/day of mexiletine, 600mg/day of mexiletine, or placebo (non-active study drug).