Accelerating Access to Critical Therapies for ALS Act This bill establishes a grant program, as well as a new center within the Food and Drug Administration (FDA), to facilitate access to investigational therapies for neurodegenerative diseases such as amyotrophic lateral sclerosis (i.e., ALS, also known as Lou Gehrig's disease, a progressive and fatal disease). Specifically, the Department of Health and Human Services (HHS) must award grants for the provision of investigational drugs for ALS and other rapidly progressing neurodegenerative diseases through an expanded access (i.e., compassionate use) program. HHS may award these grants to (1) a small business that is the sponsor of an investigational new drug application, or (2) a participating clinical trial site for such a sponsor. Additionally, HHS must establish within the FDA a Center of Excellence for Neurodegenerative Diseases. The center shall have duties and authorities similar to those of the FDA's Oncology Center of Excellence, which helps expedite the development of medical products and assists providers in requesting access to investigational drugs.