High dry friction requires intimate contact between two surfaces and is generally obtained using soft materials with an elastic modulus less than 10 MPa. We demonstrate that high-friction properties similar to rubberlike materials can also be obtained using microfiber arrays constructed from a stiff thermoplastic (polypropylene, 1 GPa). The fiber arrays have a smaller true area of contact than a rubberlike material, but polypropylene's higher interfacial shear strength provides an effective friction coefficient of greater than 5 at normal loads of 8 kPa. At the pressures tested, the fiber arrays showed more than an order of magnitude increase in shear resistance compared to the bulk material. Unlike softer materials, vertical fiber arrays of stiff polymer demonstrate no measurable adhesion on smooth surfaces due to high tensile stiffness.