Unfortunately, this currency is no longer in use so a current market value in comparison to the US Dollar is impossible. It cannot be exchanged for goods or services in Greece anymore so it can be deemed as being pretty much worthless. It may be worth something to a coin collector though.
When Greek joined the Euro Zone in January 2002, it decided to adopt the single European currency. Known as the 'Euro' this currency is now widely used in countries such as Germany, France and Italy.
By looking at how much the Euro compares to the US Dollar, this is the closest you will get to finding the value of the Drachmai. Have a look at an up-to-date currency converter such as the one found at this link:
In 2011, there are still some countries within the European Union that have not adopted the single currency. Some of the best examples include the United Kingdom and Poland. In the UK, political parties and many members of the public think that losing their currency to a single currency would be losing a sense of national identity.