There are two main dangers of drinking alcohol (assuming you're talking about small amounts of social drinking and not severe intoxication) during chemotherapy: the sedative effects and the effects on
1) Many medications can cause sedation including, among others, pain medications, anti-anxiety meds, anti-nausea meds, anti-histamines, some psychiatric meds and sleeping pills of course. The danger is that the sedative effects of the alcohol will be added to those of the other drugs so you'd sleep much too long or even, in extreme cases, stop breathing altogether. So while not specifically dealing with the chemotherapy, this can be a problem with other medications that the patient may be taking.
2) The liver is necessary to clean the body of many medications, including chemotherapy. Alcohol can interfere with the liver's ability to do its job and the patient can suffer. For this reason, when in doubt, don't drink alcohol.
There is also some question about whether alcohol may reduce the efficacy of some chemo medications. So if it's important to you to drink while undergoing chemotherapy, askyour doctor if that's okay, and ask there are any limits as to amount and timing.