Is it permissible to work with a foreign woman in a private office, alone, without the presence of another man, knowing that the nature of the work requires it?

It is not permissible to work with a woman in an office where unlawful privacy (khalwa (definition)) would ensue, which is the solitude of a man with a non-mahram (definition) woman without a third person present. The prophetic hadiths have warned against this, such as his (peace be upon him) saying: "No man is alone with a woman unless a mahram is with her," and "Beware! No man is alone with a woman but Satan is the third of them," and "Whoever believes in Allah and the Last Day should not be alone with a woman with whom he has no mahram."