Summary: We prove global existence from

${L}^{2}$ initial data for a nonlinear Dirac equation known as the

*W. E. Thirring* model [Ann. Phys. 3, 91–112 (1958;

Zbl 0078.44303)]. Local existence in

${H}^{s}$ for

$s>0$, and global existence for

$s>\frac{1}{2}$, has recently been proven by

*S. Selberg* and

*A. Tesfahun* [Differ. Integral Equ. 23, No. 3–4, 265–278 (2010;

Zbl 1240.35362)] where they used

${X}^{s,b}$ spaces together with a type of null form estimate. In contrast, motivated by the recent work of

*S. Machihara, K. Nakanishi* and

*K. Tsugawa* [Kyoto J. Math. 50, No. 2, 403–451 (2010;

Zbl 1248.35170)] we first prove local existence in

${L}^{2}$ by using null coordinates, where the time of existence depends on the profile of the initial data. To extend this to a global existence result we need to rule out concentration of

${L}^{2}$ norm, or charge, at a point. This is done by decomposing the solution into an approximately linear component and a component with improved integrability. We then prove global existence for all

$s\ge 0$.