Phase I Trial of Brentuximab Vedotin for Refractory Chronic Graft-vs.-Host Disease (GVHD)

This study is looking for the highest dose of the Brentuximab Vedotin that can be administered safely without severe or unmanageable side effects in patients that have chronic Graft vs. Host Disease, not everyone who participates in this research study will receive the same dose of the study drug. The dose each patient will get depends on the number of participants who have been enrolled in the study prior and how well they have tolerated their doses. Each patient will receive a dose of Brentuximab Vedotin every 3 weeks. Brentuximab Vedotin is administered via intravenous infusion, or IV infusion, which means directly into the vein, over a period of about 30 minutes. Each cycle is 21 days long. Each patient will undergo the following tests and procedures when they come into the clinic to receive each dose of Brentuximab Vedotin: Days 1, 8, and 15 of 1st 2 cycles: * Physical exam, which includes height, weight, body surface area and vital signs. * A medical history, which includes questions about your health, current medications, and any allergies. * Performance status, which evaluates how participant are able to carry on with your usual activities. * Routine blood tests to test overall health (about 1 teaspoon of blood) Assessment of side effects- physician will evaluate the patient's current health and ask questions to see there are any experienced side effects from taking the study drug. Only Day 1 of 1st 3 cycles: * Research blood draws for biomarker and PK assessments (pharmacokinetic assessments that measure the level of drug in the patient's blood) (about 4 teaspoons of blood) * Biomarker studies blood draw (about 4 teaspoons) Viral monitoring blood tests to make sure each patient has not developed any new viruses as a result of treatment (about 4 teaspoons of blood) * Chronic GVHD assessments: The patient's physician may need to perform other tests to confirm the diagnosis of acute GVHD. These can include more blood tests, imaging studies, and possibly biopsies of affected organs. The exact tests will be determined by the patient's physician Planned Follow-up: If the patient's physician believes the patient is responding well to treatment, the patient may receive up to 16 cycles of Brentuximab Vedotin. The Investigator would like to keep track of patient's medical condition for 12 months after the patient has completed the first 2 cycles of treatment, no matter if the patient receives more doses or not. The Investigator would like to do this by calling the patient on the telephone to see how he/she is doing. Keeping in touch with patient and checking the condition helps the Investigator look at the long-term effects of the research study.