HIV-1 infected patients after being treated with potent combinations of antiretroviral drugs for 2-6 months typically reach a state in which virus can no longer be detected within their blood. These patients with undetectable virus occasionally have viral load measurements that are above the limit of detection of current assays. Such measurements are called blips. Here we examine the possibility that such blips represent infrequent measurements taken during a period of time in which there is a transient elevation of virus in the patient's blood, i.e., a so-called transient episode of viremia. By analyzing time series of blips from a large number of patients, we conclude that transient episodes of viremia exist and that on average they extend for a period of about 3 weeks.