My friends plan to get married in Kenya on our vacation next month. 
They are complying with all of Kenya's laws for foreign citizens
getting married there.  Will this marriage be recognized in the United
States?

If your friends comply with the marital laws of Kenya, their marriage
should be legally valid in the United States.

From the Bureau of Consular Affairs (part of the U.S. Department of State website):

"The validity of marriages abroad is not dependent upon the presence
of an American diplomatic or consular officer, but upon adherence to
the laws of the country where the marriage is performed...

In general, marriages which are legally performed and valid abroad are
also legally valid in the United States. Inquiries regarding the
validity of a marriage abroad should be directed to the attorney
general of the state in the United States where the parties to the
marriage live...

The embassy or tourist information bureau of the country in which the
marriage is to be performed is the best source of information about
marriage in that country. Some general information on marriage in a
limited number of countries can be obtained from Overseas Citizens
Services, Room 4811, Department of State, Washington, DC 20520. In
addition, American embassies and consulates abroad frequently have
information about marriage in the country in which they are located."

Bureau of Consular Affairs: MARRIAGE OF UNITED STATES CITIZENS ABROAD
http://travel.state.gov/law/info/marriage/marriage_640.html

Google Web Search: valid OR validity marriage OR marriages abroad
://www.google.com/search?hl=en&q=valid+OR+validity+marriage+OR+marriages+abroad

I hope this is helpful! If anything is unclear or incomplete, please
request clarification; I'll be glad to offer further assistance before
you rate my answer.

Best regards,
pinkfreud

This is very helpful--thank you.

Thank you very much for the five stars and the nice tip!

~pinkfreud