In this article we study an asymptotic expansion for C_n, the number of connected chord diagrams on n chords. The expansion is obtained in earlier work by means of alien derivatives applied to the generating series of connected chord diagrams; we seek a combinatorial interpretation. The main outcome presented here is a new combinatorial interpretation for sequence A088221 of the On-Line Encyclopedia of Integer Sequences. We show that sequence A088221 counts pairs of connected chord diagrams (allowing empty diagrams). This gives a combinatorial interpretation for part of the closed form of the asymptotic expansion of C_n.