For t≥2, the t-independence complex Indt(G) of a graph G is the collection of all A⊆V(G) such that each connected component of the induced subgraph G[A] has at most t−1 vertices. The topology of Indt(G) is intimately related to the combinatorial property of G. In this paper, we consider the Stanley–Reisner ideal Jt(G) of Indt(G) and focus on its algebraic properties. We prove that for a chordal graph G and for all t, reg(R/Jt(G))=(t−1)νt(G) and pd(R/Jt(G))=bight(Jt(G)), where νt(G) denotes the induced matching number of the corresponding hypergraph of Jt(G), and reg, pd and bight stand for the regularity, projective dimension and big height, respectively. As a consequence of the above results, we combinatorially characterize when the Stanley–Reisner ideal of the t-independence complex of a chordal graph has a linear resolution as well as when it satisfies the Cohen–Macaulay property. The above formulas and their consequences can be seen as a nice generalization of the classical results corresponding to the edge ideals of chordal graphs.