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A simple method to achieve a large and tunable time delay of an optical signal by using a linearly chirped fiber Bragg grating (LCFBG) written in an erbium-ytterbium (Er/Yb) codoped fiber is proposed and demonstrated. The group delay response of the LCFBG can be tuned by optically pumping the LCFBG with different pumping powers, which leads to the tuning of the time delay. An LCFBG written in an Er/Yb codoped fiber is fabricated. A continuously tunable time delay up to 200 ps for a Gaussian pulse with a full-width at half-maximum of 7.6 GHz is experimentally demonstrated. The influence of the dispersion, the magnitude and group delay ripples of the LCFBG on the time delay performance, and also the stability of operation are investigated.