We report on the realization of distributed feedback quantum cascade lasers in the GaAs/AlGaAs material system. The use of a metallized surface relief grating for feedback allows a fabrication process without regrowth. A feature of this laser is that either single mode or double mode emission at lambda approximate to 10 mu m is achieved, which is typical for index coupled lasers. The coupling coefficient is measured from the mode spacing for double mode emission of a strong overcoupled laser to be kappa approximate to 24 cm(-1). The emission wavenumber can be continuously tuned with the temperature at a rate of d nu / dT approximate to 0.048 cm(-1)/K, which is in close agreement to the temperature dependence of the refractive index of GaAs.