Somewhat dated thread, but if you did not yet get your answer, the Stiller TAC 338.has a 9.165" length with standard Remington LA bolt pattern footprint whereas a garden variety Remington LA action has a 7.350" length. So yes, same bolt pattern (Remington LA), but no, not same overall action length.
As the AI chassis are typically slated specifically either for AI actions or Remington/clone actions, most likely the AI 26714 - AX Long Action .338 CIP Chassis will not accommodate the Stiller TAC 338 action without gunsnith modification. This situation is due to overall action length extending the position of the recoil lug further out than standard positioning with a factory length Remington/clone long action towards the muzzle by the length difference cited above.
Not that you would ever do this, you could actually get the Stiller TAC 338 action to bolt in if you did not include a recoil lug (very bad idea), and it would actually fit in place with the action extending into the barrel channel of the chassis; but this consideration is merely academic.
See the below link and pictures for reference for what had to be done to a similar chassis to make the longer Surgeon 1581 XL action fit into the chassis. So it can be done, but it will need gunsmith intervention, and no, the Surgeon 1581 XL-specific AI 27248 chassis will not fit the Stiller TAC 338 action in place unless additional modifications are done; already checked (said in case you managed to come across one as they are no longer made).
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