We present multiwavelength observations of a gamma-ray burst detected by INTEGRAL (GRB 030227) between 5.3 hours and ~1.7 days after the event. Here we report the discovery of a dim optical afterglow (OA) that would not have been detected by many previous searches due to its faintess (R~23). This OA was seen to decline following a power law decay with index Alpha_R= -0.95 +/- 0.16. The spectral index Beta_opt/NIR yielded -1.25 +/- 0.14. These values may be explained by a relativistic expansion of a fireball (with p = 2.0) in the cooling regime. We also find evidence for inverse Compton scattering in X-rays.