Many biological tissues are mechanically strong and stiff but can still heal from damage. By contrast, synthetic hydrogels have not shown comparable combinations of properties, as current stiffening approaches inevitably suppress the required chain/bond dynamics for self-healing. Here we show a stiff and self-healing hydrogel with a modulus of 50 MPa and tensile strength up to 4.2 MPa by polymer entanglements in co-planar nanoconfinement. This is realized by polymerizing a highly concentrated monomer solution within a scaffold of fully delaminated synthetic hectorite nanosheets, shear oriented into a macroscopic monodomain. The resultant physical gels show self-healing efficiency up to 100% despite the high modulus, and high adhesion shear strength on a broad range of substrates. This nanoconfinement approach allows the incorporation of novel functionalities by embedding colloidal materials such as MXenes and can be generalized to other polymers and solvents to fabricate stiff and self-healing gels for soft robotics, additive manufacturing and biomedical applications.