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Chapter 1 Sec 6
General Informantion
Specifications
TRANSMISSION
Clutch Wet multi-plate type
Transmission 6-speed constant
mesh
Gearshift pattern l-down, 5-up
Primary reduction 1.725 (88/51)
Final reduction 3.285 (46/14)
Gear ratios, Low 3.083 (37/12)
2nd 2.062 (33/16)
3rd 1.647 128/171
4th 1.400 (28/20)
5th 1.227 (27/22)
Top 1.095 (23/21)
Drive chain D. I. D. 50VA2
112 links
That is straight from the factory service manual for my 1996 Kat the important numbers I've got in bold, Final Reduction will be the number of teeth your sprockets should have, Chain clearly states the number of links.
NOTE: This is from a 1996 600 and will be different for your bike.
Should have pretty much the same information in your owners manual.
The "dealer" sounds like they are lying to you without remorse, or they just have no idea what they are doing.
Get them to put a new chain on there, I'd try to get sprockets out of it too, make sure there are the correct number of teeth on the sprockets, It will be stamped on there. Hope they resolve this for you, there is nothing worse than paying someone to mess things up for you, and then try to cover it up afterwords.
General Informantion
Specifications
TRANSMISSION
Clutch Wet multi-plate type
Transmission 6-speed constant
mesh
Gearshift pattern l-down, 5-up
Primary reduction 1.725 (88/51)
Final reduction 3.285 (46/14)
Gear ratios, Low 3.083 (37/12)
2nd 2.062 (33/16)
3rd 1.647 128/171
4th 1.400 (28/20)
5th 1.227 (27/22)
Top 1.095 (23/21)
Drive chain D. I. D. 50VA2
112 links
That is straight from the factory service manual for my 1996 Kat the important numbers I've got in bold, Final Reduction will be the number of teeth your sprockets should have, Chain clearly states the number of links.
NOTE: This is from a 1996 600 and will be different for your bike.
Should have pretty much the same information in your owners manual.
The "dealer" sounds like they are lying to you without remorse, or they just have no idea what they are doing.
Get them to put a new chain on there, I'd try to get sprockets out of it too, make sure there are the correct number of teeth on the sprockets, It will be stamped on there. Hope they resolve this for you, there is nothing worse than paying someone to mess things up for you, and then try to cover it up afterwords.
I called the stealership today, talked to Chris, even recorded the phone call. 
I listened as he told me that the chain length varies from bike to bike and 116 links on my bike is normal. He also told me that an 1/8" - 1/4" movement in each direction is a good tightness for the chain (after I told him that is how much travel I have when the bike is on the center stand, not even with my rump on there...) Checked my manual today only to find the above recommendations. Looks like I am making a trip down there tomorrow. 
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