This is a study to understand if taking VTX2735 is safe and effective in participants diagnosed with Cryopyrin-Associated Period Syndrome (CAPS). Approximately 10 patients will take VTX2735 Dose A or VTX2735 Dose B.

The study consists of a screening/washout period of up to 28 weeks, a 2 week treatment period, a treatment withdrawal period of up to 2 weeks, another 2 week treatment period, and a 4 week follow up period. The maximum length of treatment is 4 weeks.

Inclusion Criteria:

• At least 18 years of age
• Diagnosis of CAPS and FCAS subtype and mild clinical phenotype
• At least one flare during screening/washout
• Women must not be of childbearing potential or must agree to use two methods of highly effective contraception during the study and for 30 days after the last dose of the study product
• Men with a partner who is of childbearing potential must agree to use condoms plus another highly effective form of birth control during the study and for 90 days after the last dose of study product

Exclusion Criteria:

• Unwilling to comply with washout of anti-IL-1 therapy and tolerate symptoms of disease flare
• Moderate or severe CAPS manifestations or significant damage or any CAPS feature that presents a contraindication to washout of anti-IL-1 therapy
• Has a history of chronic or recurrent infectious disease
• Has a known immune deficiency or is immunocompromised
• Has hepatitis B or hepatitis C infection, human immunodeficiency virus (HIV), acquired immunodeficiency syndrome (AIDS), or active tuberculosis (TB)
• Has another clinically important medical disorder that would compromise safety