Under the Americans with Disabilities Act, alcoholism (and other forms of drug addiction) is a disability. The ADA defines a disability as a physical or mental impairment that substantially impairs a major life activity. Alcoholism is considered a mental impairment and the addiction-fueled over-consumption of alcohol can result in impairment of major life activities like walking, standing, thinking and so forth. The ADA prohibits employers from taking adverse employment decisions against covered employees on the basis of a disability covered by the laws. Because alcoholism is a covered disability (or a "qualified disability", in the language of the law), an employer cannot discharge or take disciplinary action against an employee for being an alcoholic. The employer may also have to provide a reasonable accommodation for the alcoholism. Taking an adverse employment action against the employee on the basis of his or her disability or failing to make a reasonable accommodation is unlawful disability discrimination.
So what if you are an alcoholic and you come to work drunk. Your employer fires you on the spot. Legal? Yes. Under the ADA, the disease of alcoholism is a disability but drinking or being intoxicated is specifically not protected. This seems logical because a worker who is drunk on the job will be a menace to himself and others, and of course will be unable to perform his duties properly. Even if the drinking is a result of the disease, the act of drinking on the job is not protected.
But what if you request time off from your employer to enter a rehab program. Your employer fires you. Legal? Probably not. This would be a request for a reasonable accommodation for the employee's disability and your employer would have to decide whether it is appropriate to offer that accommodation. Your employer may decide, for example, that taking three months off for the rehab program is not reasonable and would impose an undue burden on your employer's business. However, if a reasonable accommodation can be found (a one month part time program in the afternoons, for example) and your employer still discharges you for making the request or for taking the time off after being initially approved then the employer has very likely unlawfully discriminated against you on the basis of your disability.
The takeaway? If you are an alcoholic and request a reasonable accommodation from your employer to seek a cure, you are probably protected under the ADA. But under no circumstances should you show up to work drunk!