We have conducted a deep search for HCCN towards the dark cloud TMC-1 and several GMC's via its N(J)=1(2)->0(1) transition. HCCN was not detected in any of these sources. Towards TMC-1, assuming optically thin emission, the total column density upper limit is N_HCCN_<=2x10^12^cm^-2^, which corresponds to a fractional abundance upper limit with respect to molecular hydrogen of f_HCCN_<=2x10^-10^. We find the abundance ratio of HCN:HCCN:HCCCN in TMC-1 to be 1:<0.01:0.3, which suggests that carbon-chain growth by the addition of single carbon atoms may not be efficient under dark cloud conditions. The HCCN abundance limit also places constraints on the branching ratio for the products of the dissociative electron recombination H_3_C_2_N^+^ + e .