B737-700
Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 152; Flight Crew Type 9000
Confusion
ATC Issue All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance
Airport
We were on the ENDEE 3 Arrival into Chicago holding at POOGY at 17;000 feet. Chicago Center cleared us direct to POOGY and to 'descend via the ENDEE 3 Arrival'. After this; they handed us off to Chicago Center. We checked-in at 17;000 feet on the ENDEE 3 Arrival. Prior to our first crossing fix of NANEE; ATC asked us what altitude we were at. I responded 17;000 feet.  We were immediately belittled and sharply reminded that we were cleared to descend via the ENDEE 3.  I responded that we would make our first crossing fix at NANEE at or below 15;000 feet.  ATC immediately turned us off the arrival and was short with us.  I asked if there was a problem with our altitude. His response was to ask if we knew what a 'descend via clearance meant?' I knew that we were in compliance with all ATC instructions; therefore I did not respond. I knew a response would escalate the situation as it was clear ATC was stressed; over-reactive and may have had us confused with another aircraft.ATC may need increased staffing to relieve overworked Controllers; particularly in a high weather situation.
B737 Captain reports holding at POOGY at 17;000 feet on the ENDEE3 arrival to MDW; then told to proceed direct to POOGY and descend via the ENDEE3. The next Controller chastises the crew for not descending via the ENDEE3 (still at 17;000 feet) but not required to descend until NANEE at or below 15;000 feet. The reporter is perplexed.