B737-800
Flight Crew Air Transport Pilot (ATP)
Situational Awareness
ATC Issue All Types; Conflict Airborne Conflict; Deviation / Discrepancy - Procedural FAR; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Issued New Clearance; Flight Crew Took Evasive Action
Human Factors; Procedure
Climbing through 10;000 [feet]; ATC assigns 220 heading; then direct MNATE when able.  While climbing through 11;000 and approaching 280 knots; ATC directs; 'Expedite climb through 14;000.'  Speed intervention selected and dialed in 265 knots.  Perhaps 2-3 seconds later TCAS announces; 'Traffic.'  Target appears on ND 1;300 feet above and directly ahead perhaps 3-4 miles; maximum.  Acquired visual contact and determined that a RA was likely going to happen within seconds.  Not knowing the other aircraft type or intentions; I made the decision to stop climb below the target aircraft and turn left approximately 20 degrees.  While announcing this to the First Officer and executing the changes; but before telling him to notify ATC; ATC orders us to turn left 15 degrees and stop climb at 12;500. As this is happening; I observe the target aircraft; a Cessna Caravan; turning to a westerly heading and several skydivers departing the aircraft.  We were a bit busy at this point in time; and I did not note the exact distance or altitude separation at the closest point; but I estimate we were less than 1;000 feet below the Caravan and less than 2 miles away.  This is after deviating from the original ATC clearance to avoid a potential conflict.  Absent the deviation; a RA or worse would have been the result.  In my opinion; human error on the part of ATC. They were aware of the jump aircraft; and yet we were assigned a heading and altitude that caused a TA.
B737 Captain reports an airborne conflict with a C208 dropping skydivers.  ATC was in contact with both aircraft and issued last minute heading and altitude instructions to the reporter to avoid collision.  A TCAS TA was annunciated.