Timing chain is all lined up on 2005 cavelier and when I turn the crank once the alignment is out

To test for timing mark alignment you need to hand turn the Crank 2 full rotations when starting at Top Dead Centre. The cams turn twice for every one turn of the crank. There will be a position that isn't lined up because of the firing order.

Timing marks are stamped into the gears on the ends of the shafts. They will be a line or a dot. Look closely, they may be covered with dirt or grease. Once you have the chain or belt off, be very careful, you can damage your engine if the pistons contact the valves! The mark on the crank should be at the 12 O'clock position. If you are turning the shafts to align them and you feel strong resistance, STOP! Move one shaft or the other until the marks are aligned.

Index mark and links will only line up once per 120 rotations.
If it turns freely by wrench with the spark plugs out, it will not have any clearance issues.

Timing chain or belt? Almost all timing gears have a dot that face each other when the timing marks are lined up. If you are not carful you can damage the valves while rotating the crank and came to the lined up position. However in a perfect world the top gear can be removed when it is lined up, and reinstalled with the chain or belt in place, it will be tight but you should not need to force it. good luck

Timing belt or chain?
If you have chain align the dark mark of the chain to gear marks and release the tentioner . after you turn one time the mark wont match to the chain for long time.
if you have belt. the marks are on the dots on the head and block and will match every second turn on crankshaft
after you install belt/chain turn with hand ,don't start till you're sure the piston don't touch the valve .
with chain you can mark a dot on the block and head with marker to see if will come back to the same spot on same time crank and cam but is not accurate .
good luck

place no 1 piston at TDC compression stroke. There are procedures for the timing of the balance shafts but if it is only the timing chain I will go to that
Align uniquely coloured chain link with intake camshaft sprocket timing mark-- INT--. ( this will be pointing at the 2 o'clock position)
install timing chain and sprocket as an assembly
align first matching coloured chain link crankshaft timing mark (5 o'clock position)
align the second matching coloured chain link with exhaust cam shaft timing mark--EXH ( at the 11 o'clock position
There is a special procedure to reset the balance tensioner and it is different to the timing chain procedure.

To reset cam shaft timing chain tensioner push piston fully and turn clockwise until locked
Once the tensioner has been compressed ensure the distance from end to end is 2.83 inches . If not repeat the resetting process
vehicles 30.000 miles the tensioner is released when the engine is first started . In vehicles over 30.000 miles manually release tensioner by tapping the plunger
Note cam shaft and crank shaft sprockets bolts MUST only be used once. If you want details on the balancer chain procedure then make a comment in the box
use tension wrench and a degree gauge
cam bolts are tensioned to 63 ft lbs + 30 degrees
crank shaft pulley is tensioned to 74 ft lbs + 75 degrees

google Dodge 2.7 timing chain............select images........... the 2nd and 3rd images that come up are drawings of the timing chain assembly. Hit either one of these , and you will get full instructions for doing the job. Note ... by my eye it does not look like the timing marks on the cam pullys are exactly at the top. Slightly off to one side.

Here is a picture of the gear set. The timing marks are in the black square box.

Align the crankshaft sprocket and camshaft sprocket timing marks with the alignment tabs on the timing chain tensioner.

You will need 2 5/16 drill bits. There is a 5/16 hole in each cam gear. With the crankshaft 1/8 turn off TDC, turn the cam gears so the hole is down. Insert the drill bit into the hole and move the gear slow until the bits slides into a hole in the rear timing cover. Do this to both cam pulleys. When you have both bits installed, this will lock the cams. Don't turn the cams with the crank at TDC, It will bend valves. Once you have the cams locked, turn the crank 1/8 of a turn back to TDC. Don't go the other way. The TDC mark on the crank should be a dot on the gear and a arrow on the rear timing cover. Then after everything is lined up, Install the chain,guides and tensioner. After everything is installed, Turn the crank two revolutions, and line the crank back up to TDC. If the timing is right, you should be able to insert the drill bits in each cam gear. Hope this helps.