Inclusion Criteria:

• 1. Age 13 years and above
• 2. Clinical diagnosis of PHP (per the EuroPHP network classification guidelines1): Presence of PTH resistance or ectopic classification OR brachydactyly type E plus 2 minor criteria (TSH resistance, other hormonal resistance, developmental delay, intrauterine or post-natal growth retardation, obesity/overweight, specific facial features)
• 3. Obesity (BMI \>95th percentile for age/gender and/or ≥30 kg/m2)

Exclusion Criteria:

• 1. Use of a PDE inhibitor in the past 30 days
• 2. History of a seizure disorder unrelated to hypocalcemia
• 3. History of a cardiac arrhythmia (not including bradycardia)
• 4. Hepatic insufficiency including cirrhosis and acute hepatitis (AST or ALT \>3x upper limit of normal)
• 5. Congestive heart failure
• 6. Current cigarette use or alcohol abuse
• 7. Pregnancy or intention to become pregnant during the next year
• 8. Untreated hypothyroidism (defined as free thyroxine below the lower limit of normal)
• 9. Active peptic ulcer disease
• 10. Current use of medications known to effect theophylline levels
• 11. History of hypersensitivity to theophylline or other medication components
• 12. History of Major Depressive Disorder in the past 2 years, lifetime history of suicide attempt, history of any suicidal behavior in the past month, history of other sever psychiatric disorders (e.g. schizophrenia, bipolar disorder)
• 13. PHQ-9 score is ≥15 or suicidal ideation of type 4 or 5 (C-SSR) in the past month
• 14. Unable to comply with study procedures in the opinion of the investigator