Tretinoin and Arsenic Trioxide With or Without Gemtuzumab Ozogamicin in Treating Patients With Previously Untreated Acute Promyelocytic Leukemia

Inclusion Criteria:

* A diagnosis of APL based on the presence of the PML-RAR-alpha fusion gene by cytogenetics, polymerase chain reaction (PCR), or POD test
* Ability to understand and the willingness to sign a written informed consent document indicating that they are aware of the investigational nature of the study
* Patients in whom therapy for APL was initiated on an emergent basis are eligible (patients may have already started treatment with ATRA, ATO, and/or one dose of idarubicin due to the urgency to start therapy early)
* Women of child-bearing potential must have a negative serum pregnancy test at screening; in addition to having a negative pregnancy test confirmed at screening, all female participants of childbearing potential must have a negative pregnancy test confirmed within 48 hours prior to dosing with the study drug
* All sexually active subjects (males and females of child-bearing potential) agree to use 2 effective methods of contraception for the duration of the study

Exclusion Criteria:

* Fridericia corrected QT (QTcF) interval on the electrocardiogram (EKG) greater than 480 milliseconds
* Patients with creatinine \> 2.5 times upper limit of normal unless felt to be related the underlying leukemia by the treating physician or hemolysis or Gilbert's disease
* Patients with total bilirubin \>= 2.0 times upper limit of normal unless felt to be related the underlying leukemia by the treating physician or hemolysis or Gilbert's disease
* Patients with alanine aminotransferase (ALT)/aspartate aminotransferase (AST) \> 3 times upper limit of normal unless felt to be related the underlying leukemia by the treating physician or hemolysis or Gilbert's disease