We present the first results from the JWST program A SPectroscopic survey of biased halos In the Reionization Era (ASPIRE). This program represents an imaging and spectroscopic survey of 25 reionization-era quasars and their environments by utilizing the unprecedented capabilities of NIRCam Wide Field Slitless Spectroscopy (WFSS) mode. ASPIRE will deliver the largest ( ∼ 280 arcmin 2 ) galaxy redshift survey at 3–4 μ m among JWST Cycle 1 programs and provide extensive legacy values for studying the formation of the earliest supermassive black holes, the assembly of galaxies, early metal enrichment, and cosmic reionization. In this first ASPIRE paper, we report the discovery of a filamentary structure traced by the luminous quasar J0305–3150 and 10 [O iii ] emitters at z = 6.6. This structure has a 3D galaxy overdensity of δ _gal = 12.6 over 637 cMpc ³ , one of the most overdense structures known in the early universe, and could eventually evolve into a massive galaxy cluster. Together with existing VLT/MUSE and ALMA observations of this field, our JWST observations reveal that J0305–3150 traces a complex environment where both UV-bright and dusty galaxies are present and indicate that the early evolution of galaxies around the quasar is not simultaneous. In addition, we discovered 31 [O iii ] emitters in this field at other redshifts, 5.3 < z < 6.7, with half of them situated at z ∼ 5.4 and 6.2. This indicates that star-forming galaxies, such as [O iii ] emitters, are generally clustered at high redshifts. These discoveries demonstrate the unparalleled redshift survey capabilities of NIRCam WFSS and the potential of the full ASPIRE survey data set.