Microsoft has made some tweaks to Xbox Live and it should now be up and running.
You can keep an eye on exactly what state the service is in on the official status page, which is updated by the operations center as it irons out various niggles.
Problems came, unsurprisingly, after Halo 3 launched in the US on Tuesday, prompting an enormous surge of Master Chiefs venturing on to the service in order to shoot each other and say rude words.