Inclusion Criteria:

   - Pathologically confirmed diagnosis of non-small cell lung cancer

   - Stage IV disease by the American Joint Committee on Cancer/IASLC 7th edition proposed
   edition staging criteria

   - An EGFR sensitizing mutation must be detected in tumor tissue. Specifically, patients
   harboring the most common mutations, deletions in exon 19 or the L858R mutation in
   exon 21 are eligible. Presence of the known resistance mutation T790M as detected by
   direct tumor sequencing is not allowed. Other rare EGFR mutations may be eligible
   after discussion with the overall principal investigator

   - Age equal to or greater than 18 years

   - Measurable disease by RECIST criteria, defined as the presence of at least one lesion
   that can be accurately measured in at least one dimension (longest diameter to be
   recorded) as 10mm or greater with spiral CT scan

   - ECOG Performance status of 0, 1 or 2

   - Since prior radiation or surgery, 14 days or more must have elapsed before starting
   protocol treatment

   - No prior treatment with erlotinib, gefitinib, or other small molecule EGFR-TKIs. Prior
   treatment in the adjuvant setting is allowed if at least 1 year has elapsed since TKI
   course.

   - Adequate organ function as outlined in the protocol

   - Patients must undergo a screening eye exam to obtain approval for HCQ treatment, which
   establishes the absence of baseline conditions include macular degeneration, visual
   field changes, other retinal disease, and cataracts that interfere with required
   funduscopic examinations

   - No G6PD deficiency, as HCQ may cause hemolysis in patients with G6DP

Exclusion Criteria:

   - Symptomatic CNS metastases or newly diagnosed CNS metastases that have not yet been
   definitively treated with radiation and/or surgery. Note that patients with a history
   of CNS metastases or cord compression are allowed if they have been definitively
   treated and are clinically stable. Maintenance steroids are allowed but maintenance
   seizure medication with an EIAED is not allowed

   - Prior radiation therapy inclusive of all identified target lesions. Note that prior
   palliative radiation to bony disease, CNS disease, or a limited thoracic area is
   allowed, provided that there is measurable disease outside the field and radiation is
   completed at least two weeks prior to starting treatment and the patient has fully
   recovered from all side effects

   - Current use of hydroxychloroquine for any reason

   - Known hypersensitivity to chloroquine, hydroxychloroquine, or any closely related
   drug: erlotinib, gefitinib, or any closely related drug

   - Patients who are pregnant or breastfeeding. Female subjects of childbearing potential
   and male subjects must practice acceptable methods of birth control

   - Any evidence of clinically active interstitial lung disease. Note that patients with
   chronic, stable radiographic changes who are asymptomatic are eligible

   - Invasive malignancies within the past 3 years except for adequately treated carcinoma
   of the cervix, basal or squamous cell carcinomas of the skin

   - Evidence of any other significant clinical disorder or laboratory finding that makes
   it undesirable for the patient to participate in the study, including a prior
   diagnosis of porphyria or non-light-sensitive psoriasis, as HCQ can significantly
   exacerbate both of these conditions

   - Use of any non-FDA approved or investigational agent in 30 days or less of enrolling
   onto the trial, or failure to recover from the side effects of any of these agents

   - Penicillamine use for Wilson's disease or any other indication, as concomitant use
   with HCQ can increase toxicity to penicillamine

   - Life expectancy of less than 12 weeks