Inclusion Criteria:

- Patients must have histologically or cytologically confirmed adenocarcinoma of the
biliary ducts that is unresectable and/or metastatic; this can include unresectable
or metastatic carcinomas of the Ampulla of Vater. In addition, unresectable or
metastatic gall bladder carcinoma will be allowed

- Patients must have measurable disease, defined as at least one lesion that can be
accurately measured in at least one dimension with the longest diameter to be
recorded as >= 20 mm with conventional techniques or as >= 10 mm with spiral CT scan

- Patients may not have had prior chemotherapy for their disease; if patients have had
prior definitive surgery or prior radiation therapy, they must have fully recovered
from the effects of therapy with at least 4 weeks recovery time; for patients who
have had surgical biopsy only, they must have simply recovered

- Life expectancy of greater than 3 months

- ECOG performance status =< 2 (Karnofsky >= 60%)

- Leukocytes >= 3,000/uL

- Absolute neutrophil count >= 1,500/uL

- Platelets >= 100,000/uL

- Creatinine within normal institutional limits

- Patients may have mildly abnormal liver function defined as a total bilirubin > ULN
and =< 3x the institutional upper limits of normal (includes CTCAE v.3 grades 1-2
hyperbilirubinemia)

- The effects of Triapine on the developing human fetus at the recommended therapeutic
dose are unknown; for this reason and because heterocyclic carboxaldehyde
thiosemicarbazones as well as other therapeutic agents are known to be teratogenic,
women of child-bearing potential and men must agree to use adequate contraception
(hormonal or barrier method of birth control; abstinence) prior to study entry and
for the duration of study participation; should a woman become pregnant or suspect
she is pregnant while participating in this study, she should inform her treating
physician immediately

- When possible, patients should have an aspiration of the tumor before beginning
treatment and 24 hours after treatment has started

- Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

- Patients may not be receiving any other investigational agents

- Patients with known brain metastases should be excluded from this clinical trial
because of their poor prognosis and because they often develop progressive neurologic
dysfunction that would confound the evaluation of neurologic and other adverse events

- History of allergic reactions attributed to compounds of similar chemical or biologic
composition to Triapine or gemcitabine

- Uncontrolled intercurrent illness including, but not limited to, ongoing or active
infection, symptomatic congestive heart failure, unstable angina pectoris, or cardiac
arrhythmia

- Uncontrolled pulmonary disease including asthma, chronic bronchitis and COPD or with
requirements for chronic oxygen use

- Pregnant women are excluded from this study because Triapine is a heterocyclic
carboxaldehyde thiosemicarbazone with the potential for teratogenic or abortifacient
effects; because there is an unknown but potential risk for adverse events in nursing
infants secondary to treatment of the mother with Triapine, breastfeeding should be
discontinued if the mother is treated with Triapine; these potential risks may also
apply to other agents used in this study

- Because patients with immune deficiency are at increased risk of lethal infections
when treated with marrow-suppressive therapy, HIV-positive patients receiving
combination anti-retroviral therapy are excluded from the study because of possible
pharmacokinetic interactions with Triapine or gemcitabine administered during the
study; appropriate studies will be undertaken in patients receiving combination
anti-retroviral therapy when indicated

- Patients with G6PD deficiency will be excluded in view of the potential for
methemoglobinemia

- Psychiatric illness/social situations that would limit compliance with study
requirements