Title 14, Chapter II, Part 382 covers traveling with a service animal. Relevant sections have been reproduced below. Though not required by Part 382, it is a good idea to inform the airline that you will be traveling with your service animal. (Section 382.33 lists situations that do require advanced notice.)
§ 382.1 Purpose. The purpose of this part is to implement the Air Carrier Access Act of 1986 (49 U.S.C. 41705), which provides that no air carrier may discriminate against any otherwise qualified individual with a disability, by reason of such disability, in the provision of air transportation.
§ 382.7 General prohibition of discrimination.
(a) A carrier shall not, directly or through contractual, licensing, or other arrangements:
(1) Discriminate against any otherwise qualified individual with a disability, by reason of such disability, in the provision of air transportation;
(2) Require a person with a disability to accept special services (including, but not limited to, preboarding) not requested by the passenger;
(3) Exclude a qualified individual with a disability from or deny the person the benefit of any air transportation or related services that are available to other persons, even if there are separate or different services available for persons with a disability except when specifically permitted by another section of this part; or,
(4) Take any action adverse to an individual because of the individual’s assertion, on his or her own behalf or through or behalf of others, of rights protected by this part or the Air Carrier Access Act.
§ 382.55 Miscellaneous provisions.
(a) Carriers shall permit dogs and other service animals used by persons with a disability to accompany the persons on a flight.
(1) Carriers shall accept as evidence that an animal is a service animal identification cards, other written documentation, presence of harnesses or markings on harnesses, tags, or the credible verbal assurances of the qualified individual with a disability using the animal.
(2) Carriers shall permit a service animal to accompany a qualified individual with a disability in any seat in which the person sits, unless the animal obstructs an aisle or other area that must remain unobstructed in order to facilitate an emergency evacuation.
(3) In the event that special information concerning the transportation of animals outside the continental United States is either required to be or is provided by the carrier, the information shall be provided to all passengers traveling with animals outside the continental United States with the carrier, including those traveling with service animals.
(b) Carriers shall not require qualified individuals with a disability to sit on blankets.
(c) Carriers shall not restrict the movements of persons with a disability in terminals or require them to remain in a holding area or other location in order to be provided transportation, to receive assistance, or for other purposes, or otherwise mandate separate treatment for persons with a disability, except as permitted or required in this part.
§ 382.37 Seat assignments. (c) If a service animal cannot be accommodated at the seat location of the qualified individual with a disability whom the animal is accompanying (see § 382.55(a)(2)), the carrier shall offer the passenger the opportunity to move with the animal to a seat location, if present on the aircraft, where the animal can be accommodated, as an alternative to requiring that the animal travel with checked baggage.
§ 382.38 Seating accommodations.
(a) On request of an individual who self-identifies to a carrier as having a disability specified in this paragraph, the carrier shall provide the following seating accommodations, subject to the provisions of this section:
(3) For an individual traveling with a service animal, the carrier shall provide, as the individual requests, either a bulkhead seat or a seat other than a bulkhead seat.
§ 382.57 Charges for accommodations prohibited. Carriers shall not impose charges for providing facilities, equipment, or services that are required by this part to be provided to qualified individuals with a disability.
§ 382.3 Applicability.
(c) This part does not apply to foreign air carriers or to airport facilities outside the United States, its territories, possessions, and commonwealths.
(d) Nothing in this part shall authorize or require a carrier to fail to comply with any applicable FAA safety regulation.