GEORGETOWN, Guyana — They are the odd couple of the global oil patch: Guyana is a poor former British sugar colony. Exxon Mobil is America’s largest oil company.

They came to depend on each other after a series of extraordinary oil discoveries off Guyana’s coast transformed the small South American country’s fortunes and boosted the oil company’s assets at a time when its fortunes were flagging elsewhere.

But just as Exxon began to sell the first cargoes of Guyanese oil this year, the company found its operations at the center of the country’s biggest political crisis in decades.

After a bitterly contested — and still unresolved — election on March 2, many Guyanese are questioning whether the oil giant’s deal with their country, struck under the current government, is fair, and whether the oil proceeds will be equitably shared in a society sharply divided along ethnic lines.