HOUSTON, May 29 (Reuters) - The arbitration proceedings

in Exxon Mobil's ( XOM ) contractual dispute over Chevron's ( CVX )

planned acquisition of Hess concluded this week

and a decision is expected in about two to three months, said

Exxon senior vice president Neil Chapman on Thursday.

While speaking at a Bernstein conference, Chapman said he

was confident that a three-member arbitration panel would rule

in Exxon's favor and determine it had a right-of-first-refusal

to purchase Hess' stake in a Guyana oil joint venture that is

operated by Exxon.