While detouring weather and descending on an ATC vector an HS-125 flight crew received a TCAS TA for opposite direction traffic.

Narrative

We were descending into the Indianapolis area; working our way through significant areas of convective activity. We were planning on shooting a gap in the weather ahead. We were handed off to a new Chicago Controller. Upon checking in; it was apparent that he was busy. He issued us a heading and then kept the mike keyed for a long pause as if he was pondering whether he had issued the correct instruction. He then proceeded to authoritatively issue a descent to FL270 and a left turn to 070. This took us away from our intended gap in the weather; so I questioned whether we could continue with our prior plan. He said no; and reaffirmed his instruction. We were in the turn and descending; when we received a TA for traffic at our present altitude in the descent that was approximately 6 NM to our 10 o'clock. It appeared that our clearance had turned and descended us into opposite direction traffic. I picked up the traffic visually; and instructed my First Officer to increase the descent rate and stop the turn at about a heading of 090. Just then Center issued rushed instructions to fly heading 100. We complied with the amended clearance; and continued safely to our destination. The Controller never said a word about the incident.