I'm also a CPA and a private citizen. As a private citizen, I might offer another option that I can't recommend as a CPA. I'm sure there are many US citizens in CR, who fail to report or at least under-report their foreign income. Its not like anyone else in CR is required to report your income to the IRS on a 1099 or anything. I'm also pretty sure that it was as much pressure from the US and Canadian tax authorities as it was pressure from the DEA or local gov't that finally brought down the Brother's Fund. Many if not most of the investors were US and Canadian citizens and many if not most of them weren't reporting the interest income they were getting. The IRS was probably just drooling to get their hands on the funds financial records and their client list. I don't know if they ever did, but a lot of gringos were sweating bullets for a while there and not just because of the money they lost. Of course, that story also highlights the risk one runs by cheating on their taxes. One never knows when it might catch up with you and if it ever does watch out.
Speaking again as a CPA I can tell you that Taxman is absolutely right about being liable in both countries but also being able to deduct the taxes paid to CR from your US return.
To be a little more specific there are basically 2 ways to go about it. The simplest thing to do is to include it with your itemized deductions (line 8 of Schedule A). The major drawback here is that you'll only save to the extent of which tax bracket you're in. The second way may enable you to save 100% of what you paid in foreign income taxes (for any property tax you can only take the deduction). If the taxes you paid were less than $300 ($600 for married couples) all you have to do is report the amount on line 44 of your return. If it is more than that you'll need to fill out and file a 1116 Form. Although that form is only 2 pages long, let me warn you, again speaking as a CPA, it can be a real bear to figure out.
Here is the link to the relevant tax info
http://www.irs.gov/pub/irs-pdf/p514.pdf. Do the rest of you guys find this topic as fascinating as I do?

Have fun.