We introduce Secure Haplotype Imputation Employing Local Differential privacy (SHIELD), a program for accurately estimating the genotype of target samples at markers that are not directly assayed by array-based genotyping platforms while preserving the privacy of donors to public reference panels. At the core of SHIELD is the Li-Stephens model of genetic recombination, according to which genomic information is comprised of mosaics of ancestral haplotype fragments that coalesce via a Markov random field. We use the standard forward-backward algorithm for inferring the ancestral haplotypes of target genomes, and hence the most likely genotype at unobserved sites, using a reference panel of template haplotypes whose privacy is guaranteed by the randomized response technique from differential privacy.