A Study to Test Radium-223 With Docetaxel in Patients With Prostate Cancer

Inclusion Criteria: * Willing and able to provide written informed consent (ICF) and HIPAA authorization for the release of personal health information. A signed informed consent must be obtained before screening procedures are performed. NOTE: HIPAA authorization may be either included in the informed consent or obtained separately. * Males 18 years of age and above * Histological or cytological proof of prostate cancer * Documented progressive mCRPC based on at least one of the following criteria: 1. PSA progression defined as 25% increase over baseline value with an increase in the absolute value of at least 1.0 ng/mL that is confirmed by another PSA level with a minimum of a 1 week interval and a minimum PSA of 1.0 ng/mL. 2. Soft-tissue progression defined as an increase ≥ 20% in the sum of the LD of all target lesions based on the smallest sum LD since treatment started or the appearance of one or more new lesions. 3. Progression of bone disease (evaluable disease) or two or more new bone lesions by bone scan. * Two or more bone lesions * ECOG 0- 1 * Normal organ function with acceptable initial laboratory values within 14 days of randomization: * Albumin \> 30 g/L * ANC ≥ 1.5 x 10\^9/L * Hemoglobin ≥ 10 g/dL * Platelet count ≥ 100 x 10\^9/L * Creatinine ≤ 1.5 x the institutional upper limit of normal (ULN) * Bilirubin ≤ ULN (unless documented Gilbert's disease) * SGOT (AST) ≤ 1.5 x ULN * SGPT (ALT) ≤ 1.5 x ULN * WBC count ≥ 3 x 10\^9/L * Subjects must agree to use a medically acceptable method of birth control (e.g., spermicide in conjunction with a barrier such as a condom) or sexual abstinence for the duration of the study, including 30 days after the last dose of study drug. Sperm donation is prohibited during the study and for 30 days after the last dose of study drug. Female partners must use hormonal or barrier contraception unless postmenopausal or abstinent. * Serum testosterone \< 50 ng/dL. Subjects must continue primary androgen deprivation with an LHRH analogue (agonist or antagonist) if they have not undergone orchiectomy. * All acute toxic effects of any prior treatment have resolved to NCI-CTCAE v4.0 Grade 1 or less. * Willing and able to comply with the protocol, including follow-up visits and examinations Exclusion Criteria: * Received any other investigational therapeutic agents or other anticancer therapies within 4 weeks prior to randomization. °Note: If this requirement to have a washout of 2 weeks or 5 half-lives prior to randomization causes potential treatment delay due to Radium-223 importation timelines, the PCCTC must be contacted at pcctc@mskcc.org to request approval to randomize the subject prior to the completion of the washout. Requests for early randomization must be accompanied by written assurance by the site that the washout will be completed prior to treatment start. * Received external beam radiotherapy within the 4 weeks prior to randomization. ° Note: If prolonging randomization to complete EBRT washout causes potential treatment delay due to Radium-223 importation timelines, the PCCTC must be contacted at pcctc@mskcc.org to request approval to randomize the subject prior to the completion of the washout. Requests for early randomization must be accompanied by written assurance by the site that the washout will be completed prior to treatment start. * Has an immediate need for external beam radiotherapy. * Has received any systemic bone-seeking radiopharmaceutical in the past. * Has received any prostate cancer directed chemotherapy in the castration resistant setting. Subjects who have received up to 6 prior doses of docetaxel in the castration sensitive setting are permitted if they have not experienced disease progression within 36 weeks of last treatment with docetaxel. * Has received four or more systemic anticancer regimens for mCRPC. * Treatment with docetaxel or abiraterone for non-castrate metastatic disease is permissible and does not count towards the lines of therapy for mCRPC * A 'line' is a regimen. Combinations of hormones and other types of therapies count as single lines. * Has known Grade ≥3 docetaxel-related toxicities or docetaxel toxicity related dose interruption or discontinuation. * Has received blood transfusions or growth factors within the last 4 weeks prior to randomization. * Symptomatic nodal disease (i.e., scrotal, penile, or leg edema). * Has visceral metastases with ≥ 3 lung and/or liver metastases or individual lesion ≥2 cm, as assessed by CT scan or MRI of the chest/abdomen/pelvis within the last 8 weeks prior to randomization. * Symptomatic loco-regional disease that causes ongoing Grade 3 or Grade 4 urinary or rectal symptoms. * Subjects with a "currently active" second malignancy other than non-melanoma skin cancers or non-invasive bladder cancers or other in-situ or non-invasive malignancies. Subjects are not considered to have a "currently active" malignancy if they have completed therapy and are free of disease for ≥ 3 years. * Has imminent or established cord compression based on clinical findings and/or MRI. * Known bone marrow dysplasia * Has received any of the following in the 4 weeks prior to randomization: 5-alpha-reductase inhibitors, herbal medications, natural hormonally active foods (e.g., phytoestrogens) or other food supplements known to alter PSA in humans * Any other serious illness or medical condition that would, in the opinion of the investigator, make this protocol unreasonably hazardous, including but not limited to: * Uncontrolled infection * NYHA III or IV heart failure * Crohn's disease or those with ulcerative colitis who have not undergone a colectomy * Known active infection with HIV, Hepatitis B or Hepatitis C