I need to rent a socket to remove the front chain sprocket on a 2002 Triumph Tiger. I need to know what size wrench to use. Any help?

With the appropriate sized socket and a wrench or breaker bar. Axle nut socket sets are available in the US at most chain auto part stores for rent or purchase.

Assuming you want to remove the clutch spider, which typically is left-hand threaded onto the crank. Not knowing if it's an internal (chain drive sprocket is "outboard") or external clutch, here goes for both. After removing bar & chain.
Internal: CAREFULLY (so it doesn't fly) remove clip from crank, remove washer, clutch drum, bearing and/or rim sprocket. Remove recoil starter. Using proper tool to fit clutch "spider" and impact wrench, turn it CLOCKWISE with wrench to unthread it.
External: Remove bar & chain and recoil starter. Using tool to fit the clutch "spider" and socket on impact wrench, spin the spider off CLOCKWISE. You can then remove remainder of clutch & bearing.
Be sure to grease the bearing while it's accessible.
Starter removal avoids applying any load if the crank turns.

The timing chain on a Ford Expedition works with the camshaft and crankshaft, turning them through sprockets. The alignment with the chain and its sprockets is very precise, so replacing the chain is a very precise and difficult procedure. The chain has its own cover that you must remove to access it. Consult your mechanic before working on the timing chain. The process can vary depending on the year and engine type. Professional maintenance is always recommended.

1. Removing the Chain Cover
   • 1 Disable the truck's ignition system by disconnecting the primary electrical connectors at the ignition coil pack. Disconnect the negative battery cable before you do this.
     
   • 2 Take out the spark plugs by unplugging their wires and removing them with a socket wrench and spark plug socket.
     
   • 3 Install a compression gauge into the Number One cylinder and use a breaker bar and socket on the crankshaft's damper bolt to turn the crankshaft. Turn it until the notch in the damper aligns with the TDC mark on the front cover and compression is noted on the gauge.
     
   • 4 Drain the engine oil from the truck into a pan by removing the oil pan plug and remove the oil filter with a filter wrench.
     
   • 5 Unbolt and remove the crankshaft pulley and vibration damper; mark their positions so they can be installed the same way. Avoid turning the crankshaft as you remove the damper.
     
   • 6 Remove all accessory brackets connected to the timing chain cover by unbolting them. This includes unbolting the power steering pump; set it aside with its hoses still connected.
     
   • 7 Disconnect the camshaft position sensor's electrical connector and remove the camshaft position sensor. Disconnect the electrical connectors for the crankshaft position sensor and knock sensor.
     
   • 8 Remove the front bolts on the oil pan and the socket-head bolt--the latter requires an Allen wrench. Disconnect the heater hoses and then unbolt and pull out the heater outlet tube.
     
   • 9 Separate the timing chain cover by removing its bolts. You may need to tap it with a soft face hammer if it's stuck.
     
   Changing the Chain
   • 1 Check and see that the timing marks on the camshaft, crankshaft and balance shaft sprockets are all aligned. If not, re-install the vibration damper bolt so you can turn the crankshaft clockwise to align the marks.
     
   • 2 Remove the camshaft sprocket's mounting bolt and the camshaft position sensor's drive gear. Compress the timing chain tensioner with a screwdriver, hold the tensioner in the retracted position with a drill or Allen wrench and pull the sprocketed chain off the camshaft.
     
   • 3 Turn the camshaft until the key is facing the 12 o'clock position (straight up).
     
   • 4 Place the replacement chain on the camshaft sprocket, turn the sprocket until its timing mark faces 6 o'clock (straight down), position the chain over both sprockets with their timing marks lined up and slip the sprockets on the camshaft and crankshaft.
     
   • 5 Install the camshaft position sensor drive gear by aligning its keyway arrow with the Woodruff key on the camshaft.
     
   • 6 Install the camshaft sprocket bolt, applying a non-hardening thread-locking compound to the threads, and tighten the bolt to 30 to 36 foot-pounds.
     
   • 7 Remove the drill or wrench from the timing chain tensioner and re-install all the other parts in the reverse order of removal. This includes adding fresh engine oil and a new oil filter.
     

Before you go tearing everything apart it might help to understand how multi-speed derailleur shifting systems work.

Derailleur Adjustment: (likely cause of your problem)
http://sheldonbrown.com/derailer-adjustment.html

Shifting:
http://www.sheldonbrown.com/gears.html

Cassettes and Freehubs:
http://sheldonbrown.com/k7.html

Chains: (which also covers worn gear teeth, another possible cause)
http://sheldonbrown.com/chains.html

Of course everything requires special tools and procedures.

http://www.parktool.com/blog/repair-help
http://www.parktool.com/blog/repair-help/categories/cassette-and-freewheel-service
http://www.parktool.com/blog/repair-help/categories/derailleur-systems

Have fun.

97 foot pounds plus age make this a tough one to break loose. put it in first gear and have someone stand on the brake. a 1/2 inch air impact should help too.

I just did my front brakes yesterday and it needed a star drive ( torx wrech ) bit, not an Allen wrench

36mm most likely

The sprocket nut torque setting is 132Nm. If you are after the plastic cover torque settings, i dont think they have one. Hope this helps.

socket size is 36mm on older R1's .i dont think its changed for the newer model. u will probably need an air impact to remove it. puting the bike in first gear wont help. or u can ask somebody to push on the rear brake. if u got no air impact tool , u can put a big piece of wood between the wheels spikes and the swingarm to stop the rear from turning . use locktight when putting it back!