We report the coexistence of ferromagnetic order and superconductivity in UCoGe at ambient pressure. Magnetization measurements show that UCoGe is a weak ferromagnet with a Curie temperature T_{C}= 3 K and a small ordered moment \(m_{0}\)= 0.03 \(\mu_B\). Superconductivity is observed with a resistive transition temperature T_{s} = 0.8 K for the best sample. Thermal-expansion and specific-heat measurements provide solid evidence for bulk magnetism and superconductivity. The proximity to a ferromagnetic instability, the defect sensitivity of T_{s}, and the absence of Pauli limiting, suggest triplet superconductivity mediated by critical ferromagnetic fluctuations.