Inclusion Criteria:

- Histologically confirmed adenocarcinoma of the prostate

- Evidence of metastatic disease by the presence of soft tissue and/or bone
metastases on CT scan of the abdomen and/or pelvis, or bone scintigraphy

- Castrate-resistant disease defined by the following:

- Must have received standard-of-care androgen-deprivation treatment (ADT) (e.g.,
surgical castration, gonadotropin-releasing hormone [GnRH], or antagonist
treatment)

- Patients on concurrent GnRH analogue or antagonist must continue on this
treatment throughout this study

- Must have been treated with nonsteroidal antiandrogen with evidence of
subsequent disease progression

- Must have castration levels of testosterone (< 50 ng/dL) within the past 4 weeks

- Progressive disease while receiving ADT, defined by any 1 of the following:

- At least 2 consecutive rises in serum PSA (each value ≥ 2.0 ng/mL) obtained at a
minimum of 1-week intervals

- Measurable disease with ≥ 50% increase in the sum of the cross products of all
measurable lesions, or the development of new measurable lesions by RECIST

- The greatest diameter of a target lymph node must be ≥ 2 cm with
conventional techniques or ≥ 1 cm by spiral CT scan

- Non-measurable (bone) disease consisting of ≥ 2 new areas of uptake by bone scan
consistent with metastatic disease compared to previous imaging during
castration therapy

- Ambiguous results must be confirmed by other imaging modalities (e.g.,
X-ray, CT scan, or MRI)

- Presence of visceral metastases

- No known brain metastases

- Life expectancy ≥ 18 months by Halabi nomogram

- ECOG performance status 0-2

- WBC ≥ 2,000/mm^3

- ANC ≥ 1,500/mm^3

- Platelet count ≥ 100,000/mm^3

- Creatinine ≤ 2.0 mg/dL

- AST and ALT ≤ 1.5 times upper limit of normal

- Total bilirubin normal

- Fertile patients must agree to use effective contraception before, during, and for ≥
4 months after completion of study therapy

- No known infection with HIV 1 or HIV 2, HTLV-1, hepatitis B, or hepatitis C, or any
other potentially immunosuppressive infection

- Patients must have negative serologic testing for HIV, hepatitis B surface
antigen, and hepatitis C

- No history of autoimmune disease requiring active immunosuppressive therapy or ≥
grade 2 organ dysfunction as a result of known autoimmune disease

- Patients must have antinuclear antibody (ANA) titer < 1:320

- No other active malignancy except nonmelanoma skin cancer, carcinoma in situ of the
bladder, or other adequately treated cancer that has been free of recurrence for ≥ 3
years

- No allergy to eggs

- No known intolerance or allergic reactions to docetaxel or compounds of similar
chemical or biologic composition

- No known history of allergic or intolerable reaction to vaccinia virus vaccination
(e.g., smallpox)

- Patients or close household contacts of patients cannot have close contact with
persons with the following conditions within 3 weeks after potential vaccinia
immunization:

- History of eczema, active eczema or other acute, chronic, or exfoliative skin
conditions, including Darier's disease (e.g., atopic dermatitis, burns,
impetigo, varicella zoster, severe acne, or open wounds)

- Pregnant or nursing women

- Children under 3 years of age

- Immunodeficient or immunosuppressed persons (e.g., HIV infection, or treated for
other diseases with immunosuppressive agents)

- Any other moderate or severe acute illness until the illness resolves

- None of the following conditions within the past 6 months:

- Stroke

- Myocardial infarction

- Unstable angina

- NYHA class II-IV congestive heart failure

- Significant cardiomyopathy requiring treatment

- At least 4 weeks since prior nonsteroidal antiandrogen (e.g., flutamide) (6 weeks for
bicalutamide or nilutamide)

- More than 4 weeks since prior and no concurrent therapy with any of the following:

- Other systemic corticosteroids

- Inhaled, intranasal, or topical corticosteroids allowed

- No steroid eyedrops at least 2 weeks before and 4 weeks after protocol
vaccination

- PC-SPES

- Saw palmetto

- Megestrol

- Ketoconazole

- 5-α-reductase inhibitors

- Patients on 5-α-reductase inhibitors for > 28 days may continue these
agents throughout the study

- May not start therapy with 5-α-reductase inhibitors during study therapy

- Diethyl stilbestrol

- Any other hormonal agent or supplement with possible anticancer activity

- More than 4 weeks since prior external-beam radiation therapy

- At least 4 weeks since any prior treatment and recovered

- More than 4 weeks since surgery

- More than 6 months since prior chemotherapy

- Prior and/or concurrent bisphosphonates allowed

- More than 2 weeks since prior and no concurrent CYP3A4 substrates, inhibitors, or
inducers

- No prior chemotherapy for metastatic prostate cancer

- No prior radiotherapy to > 30% of bone marrow

- No prior anticancer vaccine

- No prior splenectomy

- No other concurrent investigational agents or anticancer therapy other than
androgen-deprivation treatment