This is a question you will ask a lot in the eight countries that use the East Caribbean dollar (EC$). All eight of these countries are former British territories, except Anguilla and Montserrat which still are territories. They are Anguilla, Antigua & Barbuda, Dominica, Grenada, Montserrat, St Kitts & Nevis, St Lucia, St Vincent & the Grenadines and have been using the EC$ since it replaced the former British West Indies Dollar in 1965.
The good news is that I found in each country the US$ was accepted just as readily as the EC$. In fact, in the touristy spots and a lot of taxis the prices were actually given in US$ instead to help the tourist out. This was kind of funny since they had to convert back, because I tried to carry EC$.
Since 1976, the EC$ has been pegged at 2.70 to each US$, but the exchange rate I was getting seems to be as low as 2.60 all the way to the official 2.70. In fact, there are several government agencies that gave the lower amount.
When visiting these countries simply ask if the price is in US$ or EC$ to make sure everyone is on the same page. I never witnessed it, but I am sure there are times one of the very few dishonest cabbies will quote a price in EC$ and then say it was in US$. Just be careful!