My previous employer had an HSA. My new employer has an Archer MSA (employer contributed only). Can I continue contributing to my HSA and receive a tax deduction?

[BMcCalpin]

The answer is "yes, sort of".

Contributions to MSAs and HSAs interact (this is to keep you from evading the contribution limits on one or the other).

See what the IRS says,

"You must reduce the amount that can be contributed (including any additional contribution) to your HSA by the amount of any contribution made to your Archer MSA (including employer contributions) for the year. A special rule applies to married people, discussed next, if each spouse has family coverage under an HDHP." (page 6 at https://www.irs.gov/pub/irs-pdf/p969.pdf).

If you are married, read the text in Pub 969 (the link above).