MEMORANDUM AND ORDER DISMISSING HABEAS PETITION
DALE S. FISCHER, District Judge.
On December 6, 2013, Juan Jose Campos ("Petitioner"), a state prisoner proceeding prose, filed his pending petition for a writ of habeas corpus by a person in state custody pursuant to 28 U.S.C. § 2254 ("Petition"). For the reasons discussed below, this action is dismissed without prejudice because the sole claim in the Petition is unexhausted.
A. Habeas Rule 4
"A discrete set of Rules governs federal habeas proceedings launched by state prisoners." See Rules Governing Section 2254 Cases in the United States District Courts, 28 foll. U.S.C. § 2254 ("Habeas Rules"); Mayle v. Felix, 545 U.S. 644, 654, 125 S.Ct. without ordering a responsive pleading where the face of the petition shows the petitioner is not entitled to relief in district court. Felix, 545 U.S. at 656. Local Rule 72-3.2 of this Court also authorizes a magistrate judge to prepare a proposed order for summary dismissal and a proposed judgment for the district judge's consideration where, as here, it plainly appears from the face of the petition that petitioner is not entitled to relief.
B. The Federal Exhaustion Doctrine
Under 28 U.S.C. § 2254, as amended by the Antiterrorism and Effective Death Penalty Act of 1996 ("AEDPA"), 110 Stat. 1214, "[a]n application for a writ of habeas corpus on behalf of a person in custody pursuant to the judgment of a State court shall not be granted unless it appears that... the applicant has exhausted the remedies available in the courts of the State[.]" 28 U.S.C. § 2254(b)(1)(A). The purpose of AEDPA's exhaustion requirement is to give the state the opportunity to pass upon and correct alleged violations of its own prisoners' federal rights. See Baldwin v. Reese, 541 U.S. 27, 29, 124 S.Ct. 1347 (2004). To provide that opportunity, a prisoner "must fairly present' his claim in each appropriate state court (including a state supreme court with powers of discretionary review), thereby alerting that court to the federal nature of the claim." Id.
Here, the pending Petition raises a single claim of ineffective assistance of counsel ("lAC"). (Pet. at 5; attached pages at 7-12.) Petitioner concedes he did not appeal his judgment of conviction, and there is no record of any state habeas petitions having been filed challenging his conviction. (Pet. at 2-3; state court records.) Consequently, the Court finds Petitioner's pending lAC claim is unexhausted because the state courts, and most importantly the California Supreme Court, have not had the opportunity to pass upon it. § 2254(b)(1)(A); Baldwin, 541 U.S. at 29.
Moreover, Petitioner's unsupported assertion that he is "currently exhausting" his IAC claim in a newly-filed habeas petition in the California Supreme Court (Pet. at 5, 8) still renders his Petition unexhausted. Because state courts "should have the first opportunity to examine the lawfulness of a state prisoner's confinement, " Batchelor v. Cupp, 693 F.2d 859, 862 (9th Cir. 1982), the exhaustion doctrine also extends to situations where the prisoner has a post-conviction challenge to his conviction still pending in the state courts. Sherwoodv. Tomkins, 716 F.2d 632, 634 (9th Cir. 1983); see also Schnepp v. Oregon, 333 F.2d 288, 288 (9th Cir. 1964). This is because "[i]f the prisoner's claim is meritorious, and if the state remedy is prompt and complete, there is no need to bring post-conviction proceedings in federal courts." Sherwood, 716 F.2d at 633 (internal quotation marks and citation omitted). Thus, to the extent Petitioner is correct that he has a habeas petition raising his lAC claim pending before the California Supreme Court, his Petition before this Court is an unexhausted petition. !d. at 633-34; Schnepp, 333 F.2d at 288.
Finally, Petitioner's accompanying motion for a stay  is denied. While district courts have the discretion in limited circumstances to hold a mixed or fully exhausted petition in abeyance pending the exhaustion ofunexhausted claims, Rhines v. Weber, 544 U.S. 269, 273-79, 125 S.Ct.1528 (2005), Kellyv. Small, 315 F.3d 1063, 1066-71 (9th Cir. 2003), King v. Ryan, 564 F.3d 1133, 1138-41 (9th Cir. 2009), a district court is "obliged to dismiss immediately" when the petition contains no exhausted claims. Jiminez v. Rice, 276 F.3d 478, 481 (9th Cir. 2001) (citation omitted); see alsoRasberryv. Garcia, 448 F.3d 1150, 1154 (9th Cir. 2006) ("Once a district court determines that a habeas petition contains only unexhausted claims, ... it may simply dismiss the habeas petition for failure to exhaust."). Petitioner, having presented a fully unexhausted Petition, is not entitled to a stay of this action because it must be dismissed. Coleman v. Thompson, 501 U.S. 722, 731, 111 S.Ct. 2546 (1991) ("a state prisoner's federal habeas petition should be dismissed if the prisoner has not exhausted available state remedies....")
For the reasons discussed above, the reference to the Magistrate Judge is vacated and the Petition is ...