We present measurements of the lowest field for flux penetration of untwinned YBa2Cu3O7 crystals near their transition temperature Tc. This field decreases linearly with increasing temperature but exhibits an anomalous change in the slope in close vicinity of Tc. Low-dose electron irradiation reduces dramatically the first field for flux penetration. We discuss these results in terms of Bean-Livingston surface barriers which are proposed to be the origin for retardation in flux entry and for irreversible phenomena in the unirradiated crystals. © 1991 The American Physical Society.