The magnetization of single-crystal HoNi2B2C has been measured as a function of applied field (H) and temperature in order to probe the interplay between superconductivity and magnetism in this complex layered system. The normal-state magnetic susceptibility of HoNi2BEC is highly anisotropic with a Curie-Weiss-like temperature dependence for H applied perpendicular to the c-axis and with a much weaker temperature dependence for H applied parallel to the c-axis, indicating that the Ho +3 magnetic moments lie predominately in the tetragonal a-b plane below 20 K. High-field magnetization (2000 Oe), low-field magnetization (20 Oe) and zero-field specific heat all give an antiferromagnetic ordering temperature of TN= 5.0 K. Remarkably, in 20 Oe applied field both superconductivity (Tc = 8.0 K) and antiferromagnetism (TN = 5.0 K) clearly make themselves manifest in the magnetization data. From these magnetization data a phase diagram in the H-T plane was constructed for both directions of applied field. This phase diagram shows a non-monotonic temperature dependence of He2 with a deep minimum at Tr~ = 5 K. The high-field magnetization data for H applied perpendicular to the c-axis also reveal a cascade of three phase transitions for T< 5 K and H< 15 000 Oe, contributing to the rich H versus T phase diagram for HoNi2BEC at low temperatures.