In xUnit.net, is it possible to run tests in order?

No, I don't believe so, but then unit tests by definition should be independent so order shouldn't matter. Where you do have a natural dependency you can't separate I'd suggest you combine the tests into one unit with multiple asserts.

There is a sample in our Samples project named PrioritizedFixtureSample which allows you to control the ordering of tests.

See the samples in our latest release: https://xunit.net/#releases