The following generalisation of the Erdős unit distance problem was recently suggested by Palsson, Senger and Sheffer. Given $k$ positive real numbers $δ_1,\dots,δ_k$, a $(k+1)$-tuple $(p_1,\dots,p_{k+1})$ in $\mathbb{R}^d$ is called a $(δ,k)$-chain if $\|p_j-p_{j+1}\| = δ_j$ for every $1\leq j \leq k$. What is the maximum number $C_k^d(n)$ of $(k,δ)$-chains in a set of $n$ points in $\mathbb{R}^d$, where the maximum is taken over all $δ$? Improving the results of Palsson, Senger and Sheffer, we essentially determine this maximum for all $k$ in the planar case. error term It is only for $k\equiv 1$ (mod) $3$ that the answer depends on the maximum number of unit distances in a set of $n$ points. We also obtain almost sharp results for even $k$ in $3$ dimension.