The input-constrained binary erasure channel (BEC) with strictly causal feedback is studied. The channel input sequence must satisfy the (0, k)-runlength limited (RLL) constraint, i.e., no more than k consecutive zeros are allowed. The feedback capacity of this channel is derived for all k≥1 Cfn(0, k)(ϵ) = max ϵH2(δ0)+Σk-1i=1(ϵi+1H2)(δi)Πi-1m=0δm)/1+Σk-1i=0(ϵi+1Πim=0δm) where ϵ is the erasure probability, ϵ=1-ϵ, H2(·) is the binary entropy function and the maximization is only over δk-1, while the other parameters δ0,..., δk-2 are simple functions of δk-1. A simple coding scheme is constructed for all k, establishing that the feedback capacity can be achieved using variable length zero-error coding. In addition, it is shown that non-causal knowledge of the erasures at the encoder does not increase the feedback capacity.