We present the discovery of PTF 10vgv, a Type Ic supernova (SN) detected by the Palomar Transient Factory, using the Palomar 48 inch telescope (P48). R-band observations of the PTF 10vgv field with P48 probe the SN emission from its very early phases (about two weeks before R-band maximum) and set limits on its flux in the week prior to the discovery. Our sensitive upper limits and early detections constrain the post-shock-breakout luminosity of this event. Via comparison to numerical (analytical) models, we derive an upper-limit of R <åisebox-0.5ex 4.5 R $_☉$ (R <i̊sebox-0.5ex 1 R $_☉$) on the radius of the progenitor star, a direct indication in favor of a compact Wolf-Rayet star. Applying a similar analysis to the historical observations of SN 1994I yields R <rs̊ebox-0.5ex 1/4 R $_☉$ for the progenitor radius of this SN.