• Phase I - Recommended Phase II dose of EPA [ Time Frame: 1 month ]
  Recommended Phase II dose of EPA will be established by using a standard 3 + 3 statistical design to determine the MTD as assessed by DLTs when administered orally in combination with a TKI in subjects with CML in stable chronic phase. Toxicity will be evaluated using the NCI Common Toxicity Criteria (CTC) version 5.0.
• Phase II - Anti-CML response to recommended Phase II dose Eicosapentaenoic Acid [ Time Frame: 1 year ]
  BCR-ABL transcript levels will be assessed every 3 months post initiation of Eicosapentaenoic Acid to assess Anti-CML response.

• Molecular responses of CML [ Time Frame: 1 year ]
  Log reduction from stable molecular response with bcr-abl PCR at MR 3 or more to bcr-abl to major molecular response (MR 4.5) or complete molecular response
• Induction of apoptosis in CML leukemia stem cell by formation of Δ12-PGJ3 and other metabolites [ Time Frame: 2 years ]
  Apoptosis will be analyzed by in vitro correlative studies using subject's plasma with effect on known leukemia cell line with CML leukemic stem cells. EPA metabolite will be examined by flow cytometry using Annexin V staining and adding serum from treated study subject to murine CML cells grown in vitro culture. The evaluation will be done at baseline, Month 1, and every 3 months up to year 2

• Number of subjects who experience treatment related Adverse Events (AEs) [ Time Frame: 2 years ]
  Using the NCI CTC Version 5.0, AEs will be assessed from the time of initiation of investigational medication
• Severity of AEs experienced by study subjects [ Time Frame: 2 years ]
  Using the NCI CTC Version 5.0, the highest grade of all treatment related AEs collected will be used to determine severity
• Study subject compliance with investigational regimen [ Time Frame: 2 years ]
  Proportion of protocol prescribed doses taken by subjects
• Molecular responses of CML [ Time Frame: 1 year ]
  Log reduction from stable molecular response with bcr-abl PCR at MR 3 or more to bcr-abl to major molecular response (MR 4.5) or complete molecular response
• Induction of apoptosis in CML leukemia stem cell by formation of Δ12-PGJ3 and other metabolites [ Time Frame: 2 years ]
  Analyzed by in vitro correlative studies using subject's plasma with effect on known leukemia cell line with CML leukemic stem cells.

• Drug: Eicosapentaenoic Acid
  Eicosapentaenoic Acid once per day orally
  Other Name: Omega-3 fatty acid
• Drug: Tyrosine kinase inhibitor
  Tyrosine kinase inhibitor to be administered at subjects' pre-study dose
  Other Names:

  • TKI
  • Imatinib
  • Dasatinib
  • Nilotinib
  • Bosutinib

Inclusion Criteria:

1. Male or female ≥18 years of age.
2. Confirmed diagnosis of CML ≥ 18 months from diagnosis.
3. Current concomitant treatment with TKI therapy (Imatinib, Dasatinib, Nilotinib or Bosutinib; excluding Ponatinib). TKI therapy should be stable (same drug and dose) for at least 3 months prior to study enrollment.

4. One of the following confirmed:

   1. BCR-ABL p210 at stable molecular disease (e.g., MMR stable but not CMR)
   2. HR but no MMR.
5. Stable molecular response defined as 2 sequential BCR-ABL p210 levels done in the same lab with less than ½ log reduction of BCR-ABL (BA) 3-6 months apart.
6. ECOG PS of ≤ 3

7. Adequate organ function, as defined by the following:

   ANC ≥ 500 cells/mm3 Platelet count ≥ 50,000 cells/mm3 Serum bilirubin ≤ 1.5 x ULN AST and ALT ≤ 2.5 x ULN Alkaline phosphatase ≤ 2.5 x ULN

8. WOCP as defined as defined as not surgically sterile or not one year post-menopausal, must have a negative result for a serum or urine pregnancy test within 7 days of initial receipt of study drug. Surgically sterile is defined as having had a hysterectomy, tubal ligation, or oophorectomy.
9. WOCP must use a medically accepted method of contraception and must agree to continued use of this method for the duration of the study and for 30 days after last dose of study drug. Acceptable methods of contraception include abstinence, barrier method with spermicide, intrauterine device (IUD) known to have a failure rate of less than 1% per year, or steroidal contraceptive (oral, transdermal, implanted, or injected) in conjunction with a barrier method.
10. Male subjects capable of producing offspring, must use a medically accepted method of birth control and agree to continued use of this method for the duration of the study and for 30 days after last dose of study drug because of the possible effects on spermatogenesis. Acceptable methods of contraception include abstinence, barrier method with spermicide, WOCP partner's use of an IUD known to have a failure rate of less than 1% per year, WOCP partner's use of steroidal contraceptive (oral, implanted or injected) in conjunction with a barrier method, WOCP partner is surgically sterile or 1 year postmenopausal. In addition, male subjects may not donate sperm for the duration of the study and for 30 days after last dose of study drug.

Exclusion Criteria:

1. Has a malignancy or infection requiring active treatment
2. Has a known HIV infection, Hepatitis B , or Hepatitis C infection
3. Has a known symptomatic congestive heart failure (CHF), unstable angina or cardiac arrhythmia
4. Is using Aspirin or NSAID or COX-I
5. Is known to be non-compliant to medications.
6. Has, in the opinion of the physician investigator, an uncontrolled medical or psychiatric disorder.
7. Has active central nervous system (CNS) leukemia.
8. Is preceding allogeneic stem HSCT.
9. Has a known T 315 I mutation.
10. Is taking FISH oil at EPA dose > 500 mg