Men or women of childbearing potential who refuse to use an adequate measure of contraception (oral contraceptives, intrauterine device, or barrier method of contraception in conjunction with spermicidal jelly) unless they have past medical history of surgical sterilization Women must not be able to become pregnant (e.g. post-menopausal for at least year, surgically sterile, or practicing adequate birth control methods) for the duration of the study. (Adequate contraception includes: oral contraception, implanted contraception, intrauterine device implanted for at least months, or barrier method in conjunction with spermicide.) For men who are not surgically sterile, agreement to use a barrier method of contraception for >= months after the last obinutuzumab dose; in addition, male patients must agree to request that their partners use an additional method of contraception, such as oral contraceptives, intrauterine device, barrier method of contraception, or spermicidal jelly For women of reproductive potential who are not surgically sterile, agreement to use two adequate methods of contraception, such as oral contraceptives, intrauterine device, or barrier method of contraception in conjunction with spermicidal jelly for >= months after the last obinutuzumab dose Female patients with childbearing potential should agree to use effective, nonhormonal means of contraception (intrauterine contraceptive device, barrier method of contraception in conjunction with spermicidal jelly or surgically sterile) during the study and for a period of at least months following the last administration of study drug For women who are not postmenopausal (i.e., < months after last menstruation) or surgically sterile (absence of ovaries and/or uterus) and who are sexually active: agreement to use an adequate method of contraception (oral contraceptives, intrauterine contraceptive device, barrier method of contraception in conjunction with spermicidal jelly) during the treatment period and for at least months after the last dose of study drug. Women of childbearing potential, be surgically sterile or agree to practice abstinence or utilize acceptable contraception (intrauterine, injectable, transdermal, or combination oral contraceptive) through -year post transplant; Males who are sexually active with women of childbearing potential must be surgically sterile or using an acceptable method of contraception (defined as barrier methods in conjunction with spermicides) from time of screening through weeks after last dose of study drug Fertile men or women of childbearing potential unless ) surgically sterile or ) using an adequate measure of contraception such as oral contraceptives, intrauterine device, or barrier method of contraception in conjunction with spermicidal jelly Men or women of childbearing potential who refuse to use an adequate measure of contraception (oral contraceptives, intrauterine device, or barrier method of contraception in conjunction with spermicidal jelly) unless they have past medical history of surgical sterilization Male or female patient who accepts and is able to use recognized effective contraception (oral contraceptives, intrauterine contraceptive device [IUCD], barrier method of contraception in conjunction with spermicidal jelly) throughout the study when relevant. For female patients of childbearing potential (defined as < years after last menstruation and not surgically sterile) and male patients, who are not surgically sterile or with female partners of childbearing potential: absence of effective, non-hormonal means of contraception (intrauterine contraceptive device, barrier method of contraception in conjunction with spermicidal gel) as defined in Appendix . Fertile men or women of childbearing potential unless ) surgically sterile or ) using an adequate measure of contraception such as oral contraceptives, intrauterine device, or barrier method of contraception in conjunction with spermicidal jelly Fertile men or women of childbearing potential unless ) surgically sterile or ) using an adequate measure of contraception such as oral contraceptives, intrauterine device, or barrier method of contraception in conjunction with spermicidal jelly Surgically sterile or agree to use effective contraception using an adequate measure of contraception such as oral contraceptives, intrauterine device, or barrier method of contraception in conjunction with spermicidal jelly while receiving obinutuzumab and >= months after the last dose of obinutuzumab for women, and months after the last dose of obinutuzumab for men Fertile men or women of childbearing potential unless ) surgically sterile or ) using an adequate measure of contraception such as oral contraceptives, intrauterine device, or barrier method of contraception in conjunction with spermicidal jelly Women must not be able to become pregnant (e.g., post-menopausal for at least year, surgically sterile, or practicing adequate birth control methods) for the duration of the study. (Adequate contraception includes: oral contraception, implanted contraception, intrauterine device implanted for at least months, or barrier method in conjunction with spermicide.) Fertile men or women of childbearing potential unless ) surgically sterile or ) using an adequate measure of contraception such as oral contraceptives, intrauterine device, or barrier method of contraception in conjunction with spermicidal jelly