This study will determine if daily application of topical oxybutynin 3% gel reduces the symptoms of primary axillary hyperhidrosis in adolescents and young adults. It will also assess the impact of daily topical oxybutynin 3% gel on Health Related Quality of Life (HRQOL); determine if daily topical oxybutynin 3% gel has a treatment effect at distant, untreated sites; and assess the local and systemic tolerability of daily topical oxybutynin 3% gel. Finally, the study will determine the treatment effect size, if one exists, in order to power a larger, placebo-controlled study in the future.