Vaccine Therapy With or Without Docetaxel in Treating Patients With Metastatic Prostate Cancer

DISEASE CHARACTERISTICS: * Diagnosis of androgen-independent metastatic adenocarcinoma of the prostate, confirmed by 1 of the following: * Histologically confirmed disease * Pathologically documented disease and clinical course consistent with prostate cancer * Castrate levels of testosterone with progressive disease by at least 1 of the following parameters: * 2 consecutively rising prostate-specific antigen levels, separated by at least 1 week, with at least 1 measurement that is 50% above the nadir reached after the last therapeutic maneuver (must be at least 5 ng/mL) * At least 1 new metastatic deposit on technetium Tc 99 bone scintigraphy * Progression of soft-tissue metastases by imaging or palpation, as indicated by: * Development of new area of malignant disease * At least 20% increase in sum of the longest dimension of target lesions * Serum testosterone less than 50 ng/dL if no prior surgical castration * Luteinizing hormone-releasing hormone therapy must continue * HLA-A2 positive * No brain metastases PATIENT CHARACTERISTICS: Age * 18 and over Performance status * ECOG 0-2 Life expectancy * More than 6 months Hematopoietic * Granulocyte count at least 1,500/mm\^3 * Lymphocyte count at least 500/mm\^3 * Platelet count at least 100,000/mm\^3 Hepatic * Bilirubin less than 1.5 mg/dL * AST and ALT less than 2.5 times upper limit of normal (ULN) * Alkaline phosphatase no greater than 2.5 times ULN OR * Hepatic alkaline phosphatase fraction less than 2.5 times ULN Renal * Creatinine no greater than 1.5 mg/dL OR * Creatinine clearance at least 40 mL/min * Proteinuria grade 0-1 OR * Protein less than 1,000 mg by 24-hour urine collection * No hematuria * No abnormal sediment unless non-renal Cardiovascular * No unstable or newly diagnosed angina pectoris * No myocardial infarction within the past 6 months * No New York Heart Association class II-IV congestive heart failure * No concurrent clinically significant cardiomyopathy requiring treatment Immunologic * No prior allergy or untoward reaction to vaccinia virus vaccination * No altered immune function, including: * Eczema * Atopic dermatitis * HIV * Autoimmune disease * Autoimmune neutropenia * Thrombocytopenia * Hemolytic anemia * Systemic lupus erythematosus * Sjogren's syndrome * Scleroderma * Myasthenia gravis * Goodpasture syndrome * Addison's disease * Hashimoto's thyroiditis * Active Graves' disease * Multiple sclerosis * No extensive psoriasis, severe acneiform rash, impetigo, varicella zoster, burns, or other traumatic or pruritic skin condition * No known allergy to eggs Other * No other malignancy within the past 2 years except nonmelanoma skin cancer or carcinoma in situ of the bladder * No other life-threatening or serious illness * No unhealed surgical scars * No household or close physical contact with persons with any of the following conditions during or for 2 weeks after study treatment: * Eczema or eczematoid skin disorders * Acute, chronic, or exfoliative skin conditions (e.g., atopic dermatitis, burns, impetigo, varicella zoster, severe acne, or other open rashes or wounds) * Pregnant or nursing women * Children under 5 years of age * Immunodeficient or immunosuppressed (including HIV positive) individuals * No history of seizures or encephalitis PRIOR CONCURRENT THERAPY: Biologic therapy * Not specified Chemotherapy * No prior taxanes for metastatic prostate cancer Endocrine therapy * See Disease Characteristics * At least 4 weeks since prior flutamide * At least 6 weeks since prior bicalutamide or nilutamide * No concurrent steroids except topical steroids, inhaled steroids for mild or moderate asthma, or decadron as premedication for chemotherapy Radiotherapy * Not specified Surgery * See Disease Characteristics * No prior splenectomy Other * Recovered from prior therapy