We present a theoretical analysis of the effect of the attochirp on the streaking time delay, intrinsic to photoionization of an atom by an attosecond laser pulse at extreme ultraviolet wavelengths superposed by a femtosecond streaking pulse. To this end, we determine the expectation value of the delay in a chirped pulse using a recently developed model formula. Results of our calculations show that the attochirp can be relevant for photoemission from the p 3 shell in argon atom at frequencies near the Cooper minimum, while it is negligible if the photoionization cross section as a function of frequency varies smoothly.