We extend the discrete-time Chandrasekhar recursions for least-squares estimation in constant parameter state-space models to a class of structured time-variant state-space models, special cases of which often arise in adaptive filtering. It can be shown that the much studied exponentially weighted recursive least-squares filtering problem can be reformulated as an estimation problem for a state-space model having this special time-variant structure. Other applications arise in the multichannel and multidimensional adaptive filtering context.