Chekov first visited the SGC in the aftermath of a fairly disastrous joint mission between SG-1 and a team of Russian officers. This began his strained relationship with then-Colonel Jack O'Neill, whom he blamed for the deaths of all but one member of the Russian team — including Colonel Alexi Zukhov, a friend of his. (SG1: "The Tomb")
He was on better terms with Dr. Daniel Jackson, however, after Daniel made an impassioned plea to Chekov for assistance in recovering Teal'c from within the Stargate; he personally oversaw the Russian DHD's delivery to Cheyenne Mountain for use in the effort. Unfortunately the DHD was destroyed in the process. (SG1: "48 Hours").
Ultimately, Chekov became a backer of the agreement between Russia and the United States of America, though he continued to insist on the full disclosure of all technology derived through the Stargate program. He was particularly upset upon learning of the prototype F-302 fighter-interceptor, for which he ultimately secured the plans along with those for the BC-303, in exchange for leasing the Russian Stargate to the United States. (SG1: "Redemption, Part 1", "Redemption, Part 2")
When the Stargate program's existence was revealed to the governments of the United Kingdom, France and China, Chekov helped to convince a skeptical Chinese Ambassador of the merits of association with the program, using the Russian example. In his view, the United States of America shouldered most of the costs and risks associated with running the program and developing related technology, while Russia still reaped many of the benefits. (SG1: "Disclosure")
After the Goa'uld managed to infiltrate both elements of The Trust and the Russian government, Chekov helped Brigadier General Jack O'Neill to avert a nuclear war between Russia and the United States of America, facilitating a direct call between O'Neill and Russian President Mikhailov. (SG1: "Full Alert")
Chekov was later involved in brokering a deal between the Russian government and the People's Republic of China, which would see the Russians begin operating their own Stargate program with Chinese support. However, he ultimately used the deal as leverage to gain additional concessions from the United States of America — this time in the form of a 304, which had been a goal of his for some time. (SG1: "Crusade")
He personally took command of the ship, named the Korolev, in time for the battle of P3Y-229. He picked up Dr. Daniel Jackson and Lt. Colonel Cameron Mitchell from the planet Camelot and headed to the newly formed Supergate. They arrived just in time for the battle. He worked with Jackson to ring a nuclear warhead onto an Ori warship while Mitchell scrambled the F-302 fighter-interceptors. Chekov's fate is ambiguous when his ship was destroyed by Ori beams; six unidentified people managed to beam out of the Korolev. (SG1: "Camelot", "Flesh and Blood")